Toric varieties paper / Bibliography.bib

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
@article {AKMS:1997,
    AUTHOR = {Avram, A. C. and Kreuzer, M. and Mandelberg, M. and Skarke,
              H.},
     TITLE = {Searching for {$K3$} fibrations},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {494},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {567--589},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {14J32 (32J18 32J81)},
  MRNUMBER = {1453773 (98g:14041)},
MRREVIEWER = {Bruce Hunt},
       DOI = {10.1016/S0550-3213(97)00214-9},
}

@article {Batyrev:1994,
    AUTHOR = {Batyrev, Victor V.},
     TITLE = {Dual polyhedra and mirror symmetry for {C}alabi-{Y}au
              hypersurfaces in toric varieties},
   JOURNAL = {J. Algebraic Geom.},
  FJOURNAL = {Journal of Algebraic Geometry},
    VOLUME = {3},
      YEAR = {1994},
    NUMBER = {3},
     PAGES = {493--535},
      ISSN = {1056-3911},
   MRCLASS = {14J32 (14M25)},
  MRNUMBER = {MR1269718 (95c:14046)},
MRREVIEWER = {I. Dolgachev},
note = {{\tt arXiv:alg-geom/9310003v1}},
}

@article {BatyrevDais:1996,
    AUTHOR = {Batyrev, Victor V. and Dais, Dimitrios I.},
     TITLE = {Strong {M}c{K}ay correspondence, string-theoretic {H}odge
              numbers and mirror symmetry},
   JOURNAL = {Topology},
  FJOURNAL = {Topology. An International Journal of Mathematics},
    VOLUME = {35},
      YEAR = {1996},
    NUMBER = {4},
     PAGES = {901--929},
      ISSN = {0040-9383},
     CODEN = {TPLGAF},
   MRCLASS = {14E15 (14J40 14M25 32J81 32S20)},
  MRNUMBER = {MR1404917 (97e:14023)},
MRREVIEWER = {I. Dolgachev},
       DOI = {10.1016/0040-9383(95)00051-8},
}

@incollection {BatyrevBorisov:1996CYCIinTV,
    AUTHOR = {Batyrev, Victor V. and Borisov, Lev A.},
     TITLE = {On {C}alabi-{Y}au complete intersections in toric varieties},
 BOOKTITLE = {Higher-dimensional complex varieties ({T}rento, 1994)},
     PAGES = {39--65},
 PUBLISHER = {de Gruyter},
   ADDRESS = {Berlin},
      YEAR = {1996},
   MRCLASS = {14J32 (14M25)},
  MRNUMBER = {MR1463173 (98j:14052)},
MRREVIEWER = {Mark Gross},
note = {{\tt arXiv:alg-geom/9412017v1}},
}

@article {BatyrevBorisov:1996STHN,
    AUTHOR = {Batyrev, Victor V. and Borisov, Lev A.},
     TITLE = {Mirror duality and string-theoretic {H}odge numbers},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {126},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {183--203},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14J32 (14M25 32J18 81T30)},
  MRNUMBER = {MR1408560 (97k:14039)},
MRREVIEWER = {Anatoly Libgober},
       DOI = {10.1007/s002220050093},
}

@incollection {Batyrev:1998,
    AUTHOR = {Batyrev, Victor V.},
     TITLE = {Stringy {H}odge numbers of varieties with {G}orenstein
              canonical singularities},
 BOOKTITLE = {Integrable systems and algebraic geometry ({K}obe/{K}yoto,
              1997)},
     PAGES = {1--32},
 PUBLISHER = {World Sci. Publ., River Edge, NJ},
      YEAR = {1998},
   MRCLASS = {14J32 (14B05 14M25)},
  MRNUMBER = {MR1672108 (2001a:14039)},
note = {{\tt arXiv:alg-geom/9711008v2}},
}

@incollection {BatyrevNill:2008,
    AUTHOR = {Batyrev, Victor V. and Nill, Benjamin},
     TITLE = {Combinatorial aspects of mirror symmetry},
 BOOKTITLE = {Integer points in polyhedra---geometry, number theory,
              representation theory, algebra, optimization, statistics},
    SERIES = {Contemp. Math.},
    VOLUME = {452},
     PAGES = {35--66},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2008},
   MRCLASS = {14J32 (14M25 52B20)},
  MRNUMBER = {MR2405763 (2009m:14059)},
MRREVIEWER = {Julianna Tymoczko},
note = {{\tt arXiv:math/0703456v2 [math.CO]}},
}

@article {Billo:1998,
    AUTHOR = {Bill{\'o}, Marco and Denef, Frederik and Fr{\`e}, Pietro and
              Pesando, Igor and Troost, Walter and Van Proeyen, Antoine and
              Zanon, Daniela},
     TITLE = {The rigid limit in special {K}\"ahler geometry~--- from
              {$K3$}-fibrations to special {R}iemann surfaces: a detailed
              case study},
   JOURNAL = {Classical Quantum Gravity},
  FJOURNAL = {Classical and Quantum Gravity},
    VOLUME = {15},
      YEAR = {1998},
    NUMBER = {8},
     PAGES = {2083--2152},
      ISSN = {0264-9381},
     CODEN = {CQGRDG},
   MRCLASS = {53C26 (53C80 81T60 83E30 83E50)},
  MRNUMBER = {1645608 (2000a:53080)},
MRREVIEWER = {Krzysztof Galicki},
       DOI = {10.1088/0264-9381/15/8/003},
}

@article {BJRR:2010a,
title={Cohomology of Line Bundles: A Computational Algorithm},
volume={51},
url={http://arxiv.org/abs/1003.5217},
abstractNote={We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds of interest are complete intersections of hypersurfaces in toric varieties supporting additional vector bundles.},
number={10},
journal={Journal of Mathematical Physics},
publisher={American Institute of Physics},
author={Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut},
year={2010}, 
pages={11}
}

@Unpublished{BJRR:2010b, 
author={Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut}, 
title={Cohomology of Line Bundles: Applications}, 
year={2010}, 
note={{\tt arXiv:1010.3717v1}}, 
abstractNote={Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute equivariant cohomology for line bundles, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrevʼs formula and its generalizations can be given a one-to-one cohomological interpretation. This paper is considered the third in the row of arXiv:1003.5217 and arXiv:1006.2392.}, 
pages={56}
}

@Unpublished{Borisov:1993,
author = {Borisov, Lev A.},
title = {Towards the mirror symmetry for {C}alabi-{Y}au complete intersections in {G}orenstein toric {F}ano varieties},
year = {1993},
note = {{\tt arXiv:alg-geom/9310001v1}},
}

@article {BorisovMavlyutov:2003,
    AUTHOR = {Borisov, Lev A. and Mavlyutov, Anvar R.},
     TITLE = {String cohomology of {C}alabi-{Y}au hypersurfaces via mirror
              symmetry},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {180},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {355--390},
      ISSN = {0001-8708},
     CODEN = {ADMTA4},
   MRCLASS = {32Q25 (14J32)},
  MRNUMBER = {MR2019228 (2005b:32056)},
MRREVIEWER = {Chien-Hao Liu},
       DOI = {10.1016/S0001-8708(03)00007-0},
}

@manual{BraunHampton:polyhedra,
  Author       = {Braun, Volker and Hampton, Marshall},
  Organization = {The Sage Development Team},
  Title        = {{\tt \verb+polyhedra+} module of {S}age},
  note         = {\url{http://www.sagemath.org/doc/reference/sage/geometry/polyhedra.html}},
  Year         = {2011},
}

@manual{BraunNovoseltsev:toric_variety,
  Author       = {Braun, Volker and Novoseltsev, Andrey Y.},
  Organization = {The Sage Development Team},
  Title        = {Toric varieties framework for {S}age},
  note         = {\url{http://www.sagemath.org/doc/reference/sage/schemes/generic/toric_variety.html}},
  Year         = {2011},
}

@article {BOKS:2007,
    AUTHOR = {Braun, Volker and Ovrut, Burt A. and Kreuzer, Maximilian and
              Scheidegger, Emanuel},
     TITLE = {Worldsheet instantons and torsion curves. {B}. {M}irror
              symmetry},
   JOURNAL = {J. High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
      YEAR = {2007},
    NUMBER = {10},
     PAGES = {023, 53},
      ISSN = {1126-6708},
   MRCLASS = {14N35 (14J32 14N10 81T30 81T45)},
  MRNUMBER = {MR2357955 (2009i:14079)},
MRREVIEWER = {Vincent Bouchard},
       DOI = {10.1088/1126-6708/2007/10/023},
}

@article {CDLS:1988,
    AUTHOR = {Candelas, P. and Dale, A. M. and L{\"u}tken, C. A. and
              Schimmrigk, R.},
     TITLE = {Complete intersection {C}alabi-{Y}au manifolds},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {298},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {493--525},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {53C55 (14J30 32J15 53C80 81E30 83E30)},
  MRNUMBER = {928308 (88m:53123)},
MRREVIEWER = {Nicholas Buchdahl},
       DOI = {10.1016/0550-3213(88)90352-5},
}

@article {CHSW:1985,
    AUTHOR = {Candelas, P. and Horowitz, Gary T. and Strominger, Andrew and
              Witten, Edward},
     TITLE = {Vacuum configurations for superstrings},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {258},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {46--74},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {83E15 (53C80 58G40 81E20 81G20)},
  MRNUMBER = {800347 (87k:83091a)},
MRREVIEWER = {Marc Henneaux},
       DOI = {10.1016/0550-3213(85)90602-9},
}


@article {CLS:1988,
    AUTHOR = {Candelas, P. and L{\"u}tken, C. A. and Schimmrigk, R.},
     TITLE = {Complete intersection {C}alabi-{Y}au manifolds. {II}. {T}hree
              generation manifolds},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {306},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {113--136},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {53C55 (14J30 32J15 53C80 83E30)},
  MRNUMBER = {952965 (89g:53102)},
MRREVIEWER = {Nicholas Buchdahl},
       DOI = {10.1016/0550-3213(88)90173-3},
}

@article {CandelasLynkerSchimmrigk:1990,
    AUTHOR = {Candelas, P. and Lynker, M. and Schimmrigk, R.},
     TITLE = {Calabi-{Y}au manifolds in weighted {${\bf P}\sb 4$}},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {341},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {383--402},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {14J30 (32J17 53C80 81T30 81T40)},
  MRNUMBER = {1067295 (91m:14062)},
MRREVIEWER = {Bruce Hunt},
       DOI = {10.1016/0550-3213(90)90185-G},
}

@article {CdlOHS:2008,
    AUTHOR = {Candelas, Philip and de la Ossa, Xenia and He, Yang-Hui and
              Szendr{\H{o}}i, Bal{\'a}zs},
     TITLE = {Triadophilia: a special corner in the landscape},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {12},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {429--473},
      ISSN = {1095-0761},
   MRCLASS = {14J32 (32Q25 81T30)},
  MRNUMBER = {2399316 (2009d:14049)},
MRREVIEWER = {Mark Gross},
}

@article {ClingherDoran:2007,
    AUTHOR = {Clingher, Adrian and Doran, Charles F.},
     TITLE = {Modular invariants for lattice polarized {$K3$} surfaces},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {55},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {355--393},
      ISSN = {0026-2285},
   MRCLASS = {14J28 (14J27)},
  MRNUMBER = {2369941 (2009a:14049)},
MRREVIEWER = {I. Dolgachev},
       DOI = {10.1307/mmj/1187646999},
}

@incollection {CDLW:2009,
    AUTHOR = {Clingher, Adrian and Doran, Charles F. and Lewis, Jacob and
              Whitcher, Ursula},
     TITLE = {Normal forms, {$K3$} surface moduli, and modular
              parametrizations},
 BOOKTITLE = {Groups and symmetries},
    SERIES = {CRM Proc. Lecture Notes},
    VOLUME = {47},
     PAGES = {81--98},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2009},
   MRCLASS = {14J15 (11F23 14H52 14J28)},
  MRNUMBER = {2500555 (2011c:14104)},
MRREVIEWER = {Jong Hae Keum},
note = {{\tt arXiv:0712.1880v1 [math.AG]}}
}
		
@book {CoxKatz:1999,
    AUTHOR = {Cox, David A. and Katz, Sheldon},
     TITLE = {Mirror symmetry and algebraic geometry},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {68},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {1999},
     PAGES = {xxii+469},
      ISBN = {0-8218-1059-6},
   MRCLASS = {14J32 (14-02 14M25 14N10 14N35 32G81 32J81 32Q25)},
  MRNUMBER = {MR1677117 (2000d:14048)},
MRREVIEWER = {Andreas Gathmann},
}

@book {CoxLittleSchenck:2011,
    AUTHOR = {Cox, David A. and Little, John and Schenck, Hal},
     TITLE = {Toric Varieties},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {124},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2011},
     PAGES = {approx. 863},
note = {Pre-publication version will be available until publication at \url{http://www.cs.amherst.edu/~dac/toric.html}},
}

@manual{Cython,
  Key          = {Cython},
  Author       = {Ewing, Greg and Bradshaw, Robert W. and Behnel, Stefan and Seljebotn, Dag S. and others},
  Title        = {{C}ython compiler ({V}ersion 0.13)},
  note         = {\url{http://www.cython.org}},
  Year         = {2010},
}

@incollection {Dixon:1988,
    AUTHOR = {Dixon, Lance J.},
     TITLE = {Some world-sheet properties of superstring compactifications,
              on orbifolds and otherwise},
 BOOKTITLE = {Superstrings, unified theories and cosmology 1987 ({T}rieste,
              1987)},
    SERIES = {ICTP Ser. Theoret. Phys.},
    VOLUME = {4},
     PAGES = {67--126},
 PUBLISHER = {World Sci. Publ., Teaneck, NJ},
      YEAR = {1988},
   MRCLASS = {81T30 (81-02)},
  MRNUMBER = {1104035 (91m:81199)},
}

@incollection {DoranMorgan:2006,
    AUTHOR = {Doran, Charles F. and Morgan, John W.},
     TITLE = {Mirror symmetry and integral variations of {H}odge structure
              underlying one-parameter families of {C}alabi-{Y}au
              threefolds},
 BOOKTITLE = {Mirror symmetry. {V}},
    SERIES = {AMS/IP Stud. Adv. Math.},
    VOLUME = {38},
     PAGES = {517--537},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2006},
   MRCLASS = {14D07 (14J32 14M25)},
  MRNUMBER = {2282973 (2008e:14010)},
MRREVIEWER = {Bal{\'a}zs Szendr{\H{o}}i},
note = {{\tt arXiv:math/0505272v1 [math.AG]}},
}

@article {DoranMorgan:2007,
    AUTHOR = {Doran, Charles F. and Morgan, John W.},
     TITLE = {Algebraic topology of {C}alabi-{Y}au threefolds in toric
              varieties},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {11},
      YEAR = {2007},
     PAGES = {597--642},
      ISSN = {1465-3060},
   MRCLASS = {32Q25 (14J32 14M25 32J25)},
  MRNUMBER = {MR2302498 (2008i:32033)},
MRREVIEWER = {Bal{\'a}zs Szendr{\H{o}}i},
       DOI = {10.2140/gt.2007.11.597},
}

@incollection {DoranNovoseltsev:2010,
    AUTHOR = {Doran, Charles F. and Novoseltsev, Andrey Y.},
     TITLE = {Closed form expressions for {H}odge numbers of complete
              intersection {C}alabi-{Y}au threefolds in toric varieties},
 BOOKTITLE = {Mirror Symmetry and Tropical Geometry},
    SERIES = {Contemporary Mathematics},
    VOLUME = {527},
     PAGES = {1--14},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2010},
   MRCLASS = {14J32},
note = {{\tt arXiv:0907.2701v2 [math.CO]}},
}

@book {Fulton:1993,
    AUTHOR = {Fulton, William},
     TITLE = {Introduction to toric varieties},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {131},
      NOTE = {The William H. Roever Lectures in Geometry},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1993},
     PAGES = {xii+157},
      ISBN = {0-691-00049-2},
   MRCLASS = {14M25 (14-02 14J30)},
  MRNUMBER = {1234037 (94g:14028)},
MRREVIEWER = {T. Oda},
}

@article {GreenePlesser:1990,
    AUTHOR = {Greene, B. R. and Plesser, M. R.},
     TITLE = {Duality in {C}alabi-{Y}au moduli space},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {338},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {15--37},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {32G81 (14J30 32G13 81T30 83E30)},
  MRNUMBER = {1059831 (91h:32018)},
MRREVIEWER = {Tristan H{\"u}bsch},
       DOI = {10.1016/0550-3213(90)90622-K},
}

@article {GrossSiebert:2006,
    AUTHOR = {Gross, Mark and Siebert, Bernd},
     TITLE = {Mirror symmetry via logarithmic degeneration data. {I}},
   JOURNAL = {J. Differential Geom.},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {72},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {169--338},
      ISSN = {0022-040X},
     CODEN = {JDGEAS},
   MRCLASS = {14J32 (32Q25)},
  MRNUMBER = {2213573 (2007b:14087)},
MRREVIEWER = {Diego Matessi},
}

@article {GrossSiebert:2010,
    AUTHOR = {Gross, Mark and Siebert, Bernd},
     TITLE = {Mirror symmetry via logarithmic degeneration data, {II}},
   JOURNAL = {J. Algebraic Geom.},
  FJOURNAL = {Journal of Algebraic Geometry},
    VOLUME = {19},
      YEAR = {2010},
    NUMBER = {4},
     PAGES = {679--780},
      ISSN = {1056-3911},
   MRCLASS = {14J33 (14C30 14F40)},
  MRNUMBER = {2669728},
}

@article {HuLiuYau:2002,
    AUTHOR = {Hu, Yi and Liu, Chien-Hao and Yau, Shing-Tung},
     TITLE = {Toric morphisms and fibrations of toric {C}alabi-{Y}au
              hypersurfaces},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {6},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {457--506},
      ISSN = {1095-0761},
   MRCLASS = {14M25 (14J32 32Q25)},
  MRNUMBER = {1957668 (2003m:14084)},
MRREVIEWER = {Dmitry A. Timash{\"e}v},
note = {{\tt arXiv:math/0010082v2 [math.AG]}},
}

@article {KKRS:2005,
    AUTHOR = {Klemm, Albrecht and Kreuzer, Maximilian and Riegler, Erwin and
              Scheidegger, Emanuel},
     TITLE = {Topological string amplitudes, complete intersection
              {C}alabi-{Y}au spaces and threshold corrections},
   JOURNAL = {J. High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
      YEAR = {2005},
    NUMBER = {5},
     PAGES = {023, 116 pp. (electronic)},
      ISSN = {1126-6708},
   MRCLASS = {81T45 (14J32 32Q25 81T30)},
  MRNUMBER = {MR2155395 (2006h:81263)},
MRREVIEWER = {Marcel L. Vonk},
       DOI = {10.1088/1126-6708/2005/05/023},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1088/1126-6708/2005/05/023},
note = {{\tt arXiv:hep-th/0410018v2}},
}

@Unpublished{Kreuzer:2008,
author = {Kreuzer, Maximilian},
title = {On the Statistics of Lattice Polytopes},
year = {2008},
note = {{\tt arXiv:0809.1188v1 [math.AG]}},
}

@article {KRS:2003,
    AUTHOR = {Kreuzer, Maximilian and Riegler, Erwin and Sahakyan, David A.},
     TITLE = {Toric complete intersections and weighted projective space},
   JOURNAL = {J. Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {46},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {159--173},
      ISSN = {0393-0440},
     CODEN = {JGPHE5},
   MRCLASS = {14J32 (14M25 81T30)},
  MRNUMBER = {MR1967149 (2004h:14044)},
MRREVIEWER = {Dimitrios I. Dais},
       DOI = {10.1016/S0393-0440(02)00124-9},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1016/S0393-0440(02)00124-9},
note = {{\tt arXiv:math/0103214v3 [math.AG]}},
}

@article {KreuzerSkarke:1997,
    AUTHOR = {Kreuzer, Maximilian and Skarke, Harald},
     TITLE = {On the classification of reflexive polyhedra},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {185},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {495--508},
      ISSN = {0010-3616},
     CODEN = {CMPHAY},
   MRCLASS = {32J18 (14J32 14M25 32J81)},
  MRNUMBER = {1463052 (98f:32029)},
MRREVIEWER = {Bruce Hunt},
       DOI = {10.1007/s002200050100},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1007/s002200050100},
note = {{\tt arXiv:hep-th/9512204v2}},
}

@article {KreuzerSkarke:1998,
    AUTHOR = {Kreuzer, Maximilian and Skarke, Harald},
     TITLE = {Classification of reflexive polyhedra in three dimensions},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {2},
      YEAR = {1998},
    NUMBER = {4},
     PAGES = {853--871},
      ISSN = {1095-0761},
   MRCLASS = {14M25 (14J30 14J32)},
  MRNUMBER = {1663339 (99m:14100)},
MRREVIEWER = {Sandra Di Rocco},
note = {{\tt arXiv:hep-th/9805190v1}},
}

@article {KreuzerSkarke:2002,
    AUTHOR = {Kreuzer, Maximilian and Skarke, Harald},
     TITLE = {Complete classification of reflexive polyhedra in four
              dimensions},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {4},
      YEAR = {2002},
    NUMBER = {6},
     PAGES = {1209--1230},
      ISSN = {1095-0761},
   MRCLASS = {52B20 (14J32 14J45 14M25)},
  MRNUMBER = {1894855 (2003e:52020)},
MRREVIEWER = {Alexander A. Borisov},
note = {{\tt arXiv:hep-th/0002240v1}},
}

@book{LaTeXCompanion,
author = {Frank Mittelbach and Michel Goossens},
title = {The {\LaTeX} Companion},
edition = 2,
note = {With Johannes Braams, David Carlisle, and Chris Rowley},
series = {Tools and Techniques for Computer Typesetting},
publisher = {Addison-Wesley},
address = {Boston, Massachusetts},
year = 2004,
pagenums = {1120},
bibliography = {yes},
index = {yes},
isbn = {0-201-36299-6},
} 

@article {LercheVafaWarner:1989,
    AUTHOR = {Lerche, Wolfgang and Vafa, Cumrun and Warner, Nicholas P.},
     TITLE = {Chiral rings in {$N=2$} superconformal theories},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {324},
      YEAR = {1989},
    NUMBER = {2},
     PAGES = {427--474},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {81T40 (58C27 58C28 83E30)},
  MRNUMBER = {1025424 (91d:81132)},
MRREVIEWER = {Kenichiro Aoki},
       DOI = {10.1016/0550-3213(89)90474-4},
}

@manual{Macaulay2,
  Key          = {Macaulay2},
  Author       = {Grayson, Daniel R. and Stillman, Michael E. and others},
  Title        = {{M}acaulay2, a software system for research in algebraic geometry ({V}ersion 1.4)},
  note         = {\url{http://www.math.uiuc.edu/Macaulay2/}},
  Year         = {2010},
}

@article {Magma,
    AUTHOR = {Bosma, Wieb and Cannon, John and Playoust, Catherine},
     TITLE = {The {M}agma algebra system. {I}. {T}he user language},
      NOTE = {Computational algebra and number theory (London, 1993)},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {24},
      YEAR = {1997},
    NUMBER = {3--4},
     PAGES = {235--265},
      ISSN = {0747-7171},
   MRCLASS = {68Q40},
  MRNUMBER = {MR1484478},
       DOI = {10.1006/jsco.1996.0125},
       URL = {http://dx.doi.org/10.1006/jsco.1996.0125},
}

@manual{Maple,
  Key          = {Maple},
  Organization = {Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario},
  Title        = {{M}aple ({V}ersion 11)},
  note         = {{\tt http://www.maplesoft.com/products/Maple/}},
  Year         = {2007},
}

@book {Mavlyutov:2000,
    AUTHOR = {Mavlyutov, Anvar R.},
     TITLE = {Toric geometry and mirror symmetry},
      NOTE = {Thesis (Ph.D.)--University of Massachusetts Amherst},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2000},
     PAGES = {136},
      ISBN = {978-0599-95758-9},
   MRCLASS = {Thesis},
  MRNUMBER = {2701382},
       URL =
              {http://gateway.proquest.com.login.ezproxy.library.ualberta.ca/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:9988821},
}

@article{Merali:2010,
author = {Merali, Zeeya},
doi = {10.1038/467775a},
issn = {0028-0836},
journal = {Nature},
month = oct,
number = {7317},
pages = {775--777},
title = {{Computational science: Error}},
url = {http://www.nature.com/doifinder/10.1038/467775a},
volume = {467},
year = {2010},
note = {\url{http://www.nature.com/doifinder/10.1038/467775a}},
}

@book {MSClay:2003,
    AUTHOR = {Hori, Kentaro and Katz, Sheldon and Klemm, Albrecht and
              Pandharipande, Rahul and Thomas, Richard and Vafa, Cumrun and
              Vakil, Ravi and Zaslow, Eric},
     TITLE = {Mirror symmetry},
    SERIES = {Clay Mathematics Monographs},
    VOLUME = {1},
      NOTE = {With a preface by Vafa},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2003},
     PAGES = {xx+929},
      ISBN = {0-8218-2955-6},
   MRCLASS = {14J32 (14N35 32Q25 81T30 81T60)},
  MRNUMBER = {2003030 (2004g:14042)},
MRREVIEWER = {Marcos Mari{\~n}o},
}

@Unpublished{NillSchepers:2010,
author = {Nill, Benjamin and Schepers, Jan},
title = {Gorenstein polytopes and their stringy E-functions},
year = {2010},
note = {{\tt arXiv:1005.5158v1 [math.CO]}},
}

@manual{Novoseltsev:lattice_polytope,
  Author       = {Novoseltsev, Andrey Y.},
  Organization = {The Sage Development Team},
  Title        = {{\tt \verb+lattice_polytope+} module of {S}age},
  note         = {\url{http://www.sagemath.org/doc/reference/sage/geometry/lattice_polytope}},
  Year         = {2011},
}

@book {Oda:1988,
    AUTHOR = {Oda, Tadao},
     TITLE = {Convex bodies and algebraic geometry},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results
              in Mathematics and Related Areas (3)]},
    VOLUME = {15},
      NOTE = {An introduction to the theory of toric varieties,
              Translated from Japanese},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1988},
     PAGES = {viii+212},
      ISBN = {3-540-17600-4},
   MRCLASS = {14L32 (14-02 52A25 52A43)},
  MRNUMBER = {922894 (88m:14038)},
MRREVIEWER = {I. Dolgachev},
}
	
@article {PALP,
    AUTHOR = {Kreuzer, Maximilian and Skarke, Harald},
     TITLE = {P{ALP}: a package for analysing lattice polytopes with
              applications to toric geometry},
   JOURNAL = {Comput. Phys. Comm.},
  FJOURNAL = {Computer Physics Communications. An International Journal and
              Program Library for Computational Physics and Physical
              Chemistry},
    VOLUME = {157},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {87--106},
      ISSN = {0010-4655},
     CODEN = {CPHCBZ},
   MRCLASS = {52B20 (14M25)},
  MRNUMBER = {MR2033673 (2004j:52014)},
       DOI = {10.1016/S0010-4655(03)00491-0},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1016/S0010-4655(03)00491-0},
note = {{\tt arXiv:math/0204356v1 [math.NA]}},
}

@article {PerevalovSkarke:1997,
    AUTHOR = {Perevalov, Eugene and Skarke, Harald},
     TITLE = {Enhanced gauge symmetry in type {II} and {F}-theory
              compactifications: {D}ynkin diagrams from polyhedra},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {505},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {679--700},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {14J32 (14M25 81T30)},
  MRNUMBER = {1490785 (99a:14058)},
MRREVIEWER = {Mark Gross},
       DOI = {10.1016/S0550-3213(97)00477-X},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1016/S0550-3213(97)00477-X},
note = {{\tt arXiv:hep-th/9704129v2}},
}

@manual{Python,
  Key          = {Python},
  Author       = {van Rossum, Guido and others},
  Organization = {Python Software Foundation},
  Title        = {{P}ython programming language ({V}ersion 2.7.1)},
  note         = {\url{http://www.python.org}},
  Year         = {2010},
}

@Unpublished{Rohsiepe:2004,
author = {Rohsiepe, Falk},
title = {Lattice polarized toric {K}3 surfaces},
year = {2004},
note = {{\tt arXiv:hep-th/0409290v1}},
}

@Unpublished{Rossi:2010,
author = {Rossi, Michele},
title = {Homological Type of Geometric Transitions},
year = {2010},
note = {{\tt arXiv:1001.0457v3 [math.AG]}},
}

@manual{Sage,
  Key          = {Sage},
  Author       = {Stein, William A. and others},
  Organization = {The Sage Development Team},
  Title        = {{S}age {M}athematics {S}oftware ({V}ersion 4.6.2)},
  note         = {\url{http://www.sagemath.org}},
  Year         = {2011},
}

@manual{SageTeX,
  Key          = {SageTeX},
  Author       = {Drake, Dan and others},
  Title        = {{S}age{T}e{X} package for \LaTeX ({V}ersion 2.3)},
  note         = {\url{https://bitbucket.org/ddrake/sagetex}},
  Year         = {2010},
}

@book {Werner:1987,
    AUTHOR = {Werner, J{\"u}rgen},
     TITLE = {Kleine {A}ufl\"osungen spezieller dreidimensionaler
              {V}ariet\"aten},
    SERIES = {Bonner Mathematische Schriften [Bonn Mathematical
              Publications], 186},
      NOTE = {Dissertation, Rheinische Friedrich-Wilhelms-Universit{\"a}t,
              Bonn, 1987},
 PUBLISHER = {Universit\"at Bonn Mathematisches Institut},
   ADDRESS = {Bonn},
      YEAR = {1987},
     PAGES = {viii+119},
   MRCLASS = {14E15 (14J30)},
  MRNUMBER = {930270 (89k:14018)},
MRREVIEWER = {I. Dolgachev},
}

@article {Wilson:1992,
    AUTHOR = {Wilson, P. M. H.},
     TITLE = {The {K}\"ahler cone on {C}alabi-{Y}au threefolds},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {107},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {561--583},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14J30 (14J15)},
  MRNUMBER = {1150602 (93a:14037)},
MRREVIEWER = {Bruce Hunt},
       DOI = {10.1007/BF01231902},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1007/BF01231902},
}
		
@article {Wilson:1993,
    AUTHOR = {Wilson, P. M. H.},
     TITLE = {Erratum: ``{T}he {K}\"ahler cone on {C}alabi-{Y}au
              threefolds'' [{I}nvent.\ {M}ath.\ {\bf 107} (1992), no.\ 3,
              561--583; {MR}1150602 (93a:14037)]},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {114},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {231--233},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14J30 (14J15)},
  MRNUMBER = {1235026 (94i:14042)},
MRREVIEWER = {Bruce Hunt},
       DOI = {10.1007/BF01232669},
       URL = {http://dx.doi.org.login.ezproxy.library.ualberta.ca/10.1007/BF01232669},
}
		
Tip: Filter by directory path e.g. /media app.js to search for public/media/app.js.
Tip: Use camelCasing e.g. ProjME to search for ProjectModifiedEvent.java.
Tip: Filter by extension type e.g. /repo .js to search for all .js files in the /repo directory.
Tip: Separate your search with spaces e.g. /ssh pom.xml to search for src/ssh/pom.xml.
Tip: Use ↑ and ↓ arrow keys to navigate and return to view the file.
Tip: You can also navigate files with Ctrl+j (next) and Ctrl+k (previous) and view the file with Ctrl+o.
Tip: You can also navigate files with Alt+j (next) and Alt+k (previous) and view the file with Alt+o.