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6-d Anomaly Cancellation / Main.bib

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@article{Grassi:2011hq,
      author         = "Grassi, Antonella and Morrison, David R.",
      title          = "{Anomalies and the Euler characteristic of elliptic
                        Calabi-Yau threefolds}",
      year           = "2011",
      eprint         = "1109.0042",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}


@article{Katz:2011qp,
      author         = "Katz, Sheldon and Morrison, David R. and Schafer-Nameki,
                        Sakura and Sully, James",
      title          = "{Tate's algorithm and F-theory}",
      journal        = "JHEP",
      volume         = "1108",
      pages          = "094",
      doi            = "10.1007/JHEP08(2011)094",
      year           = "2011",
      eprint         = "1106.3854",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}


@Article{Bershadsky:1996nh,
     author    = "Bershadsky, M. and others",
     title     = "{Geometric singularities and enhanced gauge symmetries}",
     journal   = "Nucl. Phys.",
     volume    = "B481",
     year      = "1996",
     pages     = "215-252",
     eprint    = "hep-th/9605200",
     archivePrefix = "arXiv",
     doi       = "10.1016/S0550-3213(96)90131-5",
     SLACcitation  = "%%CITATION = HEP-TH/9605200;%%"
}

@incollection {MR0393039,
    AUTHOR = {Tate, J.},
     TITLE = {Algorithm for determining the type of a singular fiber in an
              elliptic pencil},
 BOOKTITLE = {Modular functions of one variable, {IV} ({P}roc. {I}nternat.
              {S}ummer {S}chool, {U}niv. {A}ntwerp, {A}ntwerp, 1972)},
     PAGES = {33--52. Lecture Notes in Math., Vol. 476},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1975},
   MRCLASS = {14G25 (14K15)},
  MRNUMBER = {0393039 (52 \#13850)},
MRREVIEWER = {J. S. Milne},
}

@book{pre05771645,
author="Duistermaat, Johannes J.",
title="{Discrete integrable systems. QRT maps and elliptic surfaces.}",
language="English",
publisher="{Springer Monographs in Mathematics. Berlin: Springer. xxii, 627~p.}",
year="2010",
doi={10.1007/978-0-387-72923-7},
abstract="{Preliminary review / Publisher's description: The rich subject matter
    in this book brings in mathematics from different domains, especially from
    the theory of elliptic surfaces and dynamics.The material comes from the
    author’s insights and understanding of a birational transformation of
    the plane derived from a discrete sine-Gordon equation, posing the question
    of determining the behavior of the discrete dynamical system defined by the
    iterates of the map. The aim of this book is to give a complete treatment
    not only of the basic facts about QRT maps, but also the background theory
    on which these maps are based. Readers with a good knowledge of algebraic
    geometry will be interested in Kodaira’s theory of elliptic surfaces
    and deal with the collection of nontrivial applications presented here.
    While prerequisites for some readers will demand their knowledge of quite a
    bit of algebraic- and complex analytic geometry, different categories of
    readers will be able to become familiar with any selected interest in the
    book without having to make an extensive journey through the literature.}",
classmath="{*14-02 (Research monographs (algebraic geometry))
14H70 (Automorphisms of curves)
14J27 (Elliptic surfaces)
}",
}

@ARTICLE{2000math.....10082H,
   author = {{Hu}, Y. and {Liu}, C.-H. and {Yau}, S.-T.},
    title = "{Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces}",
  journal = {ArXiv Mathematics e-prints},
   eprint = {arXiv:math/0010082},
 keywords = {Mathematics - Algebraic Geometry, High Energy Physics - Theory},
     year = 2000,
    month = oct,
   adsurl = {http://adsabs.harvard.edu/abs/2000math.....10082H},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@incollection {Yau1,
    AUTHOR = {Yau, Shing-Tung},
     TITLE = {Compact three-dimensional {K}\"ahler manifolds with zero
              {R}icci curvature},
 BOOKTITLE = {Symposium on anomalies, geometry, topology ({C}hicago, {I}ll.,
              1985)},
     PAGES = {395--406},
 PUBLISHER = {World Sci. Publishing},
   ADDRESS = {Singapore},
      YEAR = {1985},
   MRCLASS = {53C55 (81E20 83E15)},
  MRNUMBER = {MR850873 (87g:53101)},
MRREVIEWER = {Pankaj Topiwala},
}
                
@Article{Morrison:2011mb,
     author    = "Morrison, David R. and Taylor, Washington",
     title     = "{Matter and singularities}",
     year      = "2011",
     eprint    = "1106.3563",
     archivePrefix = "arXiv",
     primaryClass  =  "hep-th",
     SLACcitation  = "%%CITATION = 1106.3563;%%"
}

@Article{KreuzerSkarkeReflexive,
     author    = "Kreuzer, Maximilian and Skarke, Harald",
     title     = "{Complete classification of reflexive polyhedra in four
                  dimensions}",
     journal   = "Adv. Theor. Math. Phys.",
     volume    = "4",
     year      = "2002",
     pages     = "1209-1230",
     eprint    = "hep-th/0002240",
     archivePrefix = "arXiv",
     SLACcitation  = "%%CITATION = HEP-TH/0002240;%%"
}


@Article{Braun:2007vy,
     author    = "Braun, Volker and Kreuzer, Maximilian and Ovrut, Burt A.
                  and Scheidegger, Emanuel",
     title     = "Worldsheet Instantons and Torsion Curves, Part B: Mirror
                  Symmetry",
     journal   = "JHEP",
     volume    = "10",
     year      = "2007",
     pages     = "023",
     eprint    = "arXiv:0704.0449 [hep-th]",
     SLACcitation  = "%%CITATION = ARXIV:0704.0449;%%"
}

@Article{Braun:2007xh,
     author    = "Braun, Volker and Kreuzer, Maximilian and Ovrut, Burt A.
                  and Scheidegger, Emanuel",
     title     = "Worldsheet instantons and torsion curves. Part A: Direct
                  computation",
     journal   = "JHEP",
     volume    = "10",
     year      = "2007",
     pages     = "022",
     eprint    = "hep-th/0703182",
     SLACcitation  = "%%CITATION = HEP-TH/0703182;%%"
}

@Article{Braun:2007tp,
     author    = "Braun, Volker and Kreuzer, Maximilian and Ovrut, Burt A.
                  and Scheidegger, Emanuel",
     title     = "Worldsheet Instantons, Torsion Curves, and Non-Perturbative
                  Superpotentials",
     journal   = "Phys. Lett.",
     volume    = "B649",
     year      = "2007",
     pages     = "334-341",
     eprint    = "hep-th/0703134",
     SLACcitation  = "%%CITATION = HEP-TH/0703134;%%"
}


@Article{dP9Z3Z3,
  Author         = "Braun, Volker and Ovrut, Burt A. and Pantev, Tony and
                   Reinbacher, Rene",
  Title          = "Elliptic {{Calabi-Yau}} threefolds with {$\Z_3 \times
                   \Z_3$} {W}ilson lines",
  Journal        = "JHEP",
  Volume         = "12",
  Pages          = "062",
  eprint         = "hep-th/0410055",
  slaccitation   = "%%CITATION = HEP-TH 0410055;%%",
  year           = 2004
}



@article{Braun:2011hd,
      author         = "Braun, Volker",
      title          = "{The 24-Cell and Calabi-Yau Threefolds with Hodge Numbers
                        (1,1)}",
      year           = "2011",
      eprint         = "1102.4880",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@Article{Kreuzer:2002uu,
     author    = "Kreuzer, Maximilian and Skarke, Harald",
     title     = "PALP: A Package for analyzing lattice polytopes with
                  applications to toric geometry",
     journal   = "Comput. Phys. Commun.",
     volume    = "157",
     year      = "2004",
     pages     = "87-106",
     eprint    = "math.na/0204356",
     SLACcitation  = "%%CITATION = MATH.NA 0204356;%%"
}

@article{Cox:1993fz,
  arxivId = {alg-geom/9210008},
  author = {Cox, David A.},
  title = {The Homogeneous Coordinate Ring of a Toric Variety, Revised Version},
  year = {1993}
}

@manual{BraunHampton:polyhedra,
  Author       = {Braun, Volker and Hampton, Marshall},
  Organization = {The Sage Development Team},
  Title        = {Polyhedra module of {S}age},
  note         = {{\tt http://sagemath.org/doc/reference/sage/geometry/polyhedra.html}},
  Year         = {2010},
}

@manual{BraunNovoseltsev:toric_variety,
  Author       = {Braun, Volker and Novoseltsev, Andrey Y.},
  Organization = {The Sage Development Team},
  Title        = {Toric varieties framework for {S}age},
  note         = {{\tt http://sagemath.org/doc/reference/sage/schemes/generic/toric\_variety.html}},
  Year         = {2010},
}

@manual{Sage,
  Key          = {Sage},
  Author       = {Stein, William A. and others},
  Organization = {The Sage Development Team},
  Title        = {{S}age {M}athematics {S}oftware ({V}ersion 4.7)},
  note         = {{\tt 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         = {{\tt https://bitbucket.org/ddrake/sagetex}},
  Year         = {2010},
}




@article{Candelas:1996ht,
      author         = "Candelas, Philip and Perevalov, Eugene and Rajesh,
                        Govindan",
      title          = "{F theory duals of nonperturbative heterotic E(8) x E(8)
                        vacua in six-dimensions}",
      journal        = "Nucl.Phys.",
      volume         = "B502",
      pages          = "613-628",
      doi            = "10.1016/S0550-3213(97)00375-1",
      year           = "1997",
      eprint         = "hep-th/9606133",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}
@Article{Candelas:1997pv,
     author    = "Candelas, Philip and Perevalov, Eugene and Rajesh, Govindan
                  ",
     title     = "{Comments on A, B, C chains of heterotic and type II
                  vacua}",
     journal   = "Nucl. Phys.",
     volume    = "B502",
     year      = "1997",
     pages     = "594-612",
     eprint    = "hep-th/9703148",
     archivePrefix = "arXiv",
     doi       = "10.1016/S0550-3213(97)00374-X",
     SLACcitation  = "%%CITATION = HEP-TH/9703148;%%"
}
@article{Candelas:1997eh,
      author         = "Candelas, Philip and Perevalov, Eugene and Rajesh,
                        Govindan",
      title          = "{Toric geometry and enhanced gauge symmetry of F theory /
                        heterotic vacua}",
      journal        = "Nucl.Phys.",
      volume         = "B507",
      pages          = "445-474",
      doi            = "10.1016/S0550-3213(97)00563-4",
      year           = "1997",
      eprint         = "hep-th/9704097",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}
@article{Candelas:1997pq,
      author         = "Candelas, Philip and Skarke, Harald",
      title          = "{F theory, SO(32) and toric geometry}",
      journal        = "Phys.Lett.",
      volume         = "B413",
      pages          = "63-69",
      doi            = "10.1016/S0370-2693(97)01047-2",
      year           = "1997",
      eprint         = "hep-th/9706226",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}
@article{Candelas:1997jz,
      author         = "Candelas, Philip and Perevalov, Eugene and Rajesh,
                        Govindan",
      title          = "{Matter from toric geometry}",
      journal        = "Nucl.Phys.",
      volume         = "B519",
      pages          = "225-238",
      doi            = "10.1016/S0550-3213(98)00009-1",
      year           = "1998",
      eprint         = "hep-th/9707049",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@Article{Braun:2000hh,
     author    = "Braun, Volker and Candelas, Philip and De La Ossa, Xenia
                  and Grassi, Antonella",
     title     = "{Toric Calabi-Yau fourfolds, duality between N = 1 theories
                  and divisors  that contribute to the superpotential}",
     year      = "2000",
     eprint    = "hep-th/0001208",
     archivePrefix = "arXiv",
     SLACcitation  = "%%CITATION = HEP-TH/0001208;%%"
}

@ARTICLE{2012arXiv1201.0930G,
   author = {{Grassi}, A. and {Perduca}, V.},
    title = "{Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1201.0930},
 primaryClass = "math.AG",
 keywords = {Mathematics - Algebraic Geometry},
     year = 2012,
    month = jan,
   adsurl = {http://adsabs.harvard.edu/abs/2012arXiv1201.0930G},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@incollection {MR690264,
    AUTHOR = {Miranda, Rick},
     TITLE = {Smooth models for elliptic threefolds},
 BOOKTITLE = {The birational geometry of degenerations ({C}ambridge,
              {M}ass., 1981)},
    SERIES = {Progr. Math.},
    VOLUME = {29},
     PAGES = {85--133},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Mass.},
      YEAR = {1983},
   MRCLASS = {14J10 (14J30)},
  MRNUMBER = {690264 (84f:14024)},
MRREVIEWER = {Jonathan M. Wahl},
}
	
@Article{Vafa:1996xn,
     author    = "Vafa, Cumrun",
     title     = "{Evidence for F-Theory}",
     journal   = "Nucl. Phys.",
     volume    = "B469",
     year      = "1996",
     pages     = "403-418",
     eprint    = "hep-th/9602022",
     archivePrefix = "arXiv",
     doi       = "10.1016/0550-3213(96)00172-1",
     SLACcitation  = "%%CITATION = HEP-TH/9602022;%%"
}

@article{Morrison:1996na,
      author         = "Morrison, David R. and Vafa, Cumrun",
      title          = "{Compactifications of F theory on Calabi-Yau threefolds.
                        1}",
      journal        = "Nucl.Phys.",
      volume         = "B473",
      pages          = "74-92",
      doi            = "10.1016/0550-3213(96)00242-8",
      year           = "1996",
      eprint         = "hep-th/9602114",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}


@article{Morrison:1996pp,
      author         = "Morrison, David R. and Vafa, Cumrun",
      title          = "{Compactifications of F theory on Calabi-Yau threefolds.
                        2.}",
      journal        = "Nucl.Phys.",
      volume         = "B476",
      pages          = "437-469",
      doi            = "10.1016/0550-3213(96)00369-0",
      year           = "1996",
      eprint         = "hep-th/9603161",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}


@Article{Klemm:1996hh,
     author    = "Klemm, Albrecht and Mayr, Peter and Vafa, Cumrun",
     title     = "{BPS states of exceptional non-critical strings}",
     year      = "1996",
     eprint    = "hep-th/9607139",
     archivePrefix = "arXiv",
     SLACcitation  = "%%CITATION = HEP-TH/9607139;%%"
}


@Article{Candelas:1996su,
     author    = "Candelas, Philip and Font, Anamaria",
     title     = "{Duality between the webs of heterotic and type II vacua}",
     journal   = "Nucl. Phys.",
     volume    = "B511",
     year      = "1998",
     pages     = "295-325",
     eprint    = "hep-th/9603170",
     archivePrefix = "arXiv",
     doi       = "10.1016/S0550-3213(96)00410-5",
     SLACcitation  = "%%CITATION = HEP-TH/9603170;%%"
}

@Article{Esole:2011sm,
     author    = "Esole, Mboyo and Yau, Shing-Tung",
     title     = "{Small resolutions of SU(5)-models in F-theory}",
     year      = "2011",
     eprint    = "1107.0733",
     archivePrefix = "arXiv",
     primaryClass  =  "hep-th",
     SLACcitation  = "%%CITATION = 1107.0733;%%"
}

@Article{Vafa:2005ui,
     author    = "Vafa, Cumrun",
     title     = "{The string landscape and the swampland}",
     year      = "2005",
     eprint    = "hep-th/0509212",
     archivePrefix = "arXiv",
     SLACcitation  = "%%CITATION = HEP-TH/0509212;%%"
}


@Article{Kumar:2009ac,
     author    = "Kumar, Vijay and Morrison, David R. and Taylor, Washington
                  ",
     title     = "{Mapping 6D N = 1 supergravities to F-theory}",
     journal   = "JHEP",
     volume    = "02",
     year      = "2010",
     pages     = "099",
     eprint    = "0911.3393",
     archivePrefix = "arXiv",
     primaryClass  =  "hep-th",
     doi       = "10.1007/JHEP02(2010)099",
     SLACcitation  = "%%CITATION = 0911.3393;%%"
}

@article{Kumar:2010am,
      author         = "Kumar, Vijay and Park, Daniel S. and Taylor, Washington",
      title          = "{6D supergravity without tensor multiplets}",
      journal        = "JHEP",
      volume         = "1104",
      pages          = "080",
      doi            = "10.1007/JHEP04(2011)080",
      year           = "2011",
      eprint         = "1011.0726",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@article{Kumar:2010ru,
      author         = "Kumar, Vijay and Morrison, David R. and Taylor,
                        Washington",
      title          = "{Global aspects of the space of 6D N = 1 supergravities}",
      journal        = "JHEP",
      volume         = "1011",
      pages          = "118",
      doi            = "10.1007/JHEP11(2010)118",
      year           = "2010",
      eprint         = "1008.1062",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@article{Seiberg:2011dr,
      author         = "Seiberg, Nathan and Taylor, Washington",
      title          = "{Charge Lattices and Consistency of 6D Supergravity}",
      journal        = "JHEP",
      volume         = "1106",
      pages          = "001",
      doi            = "10.1007/JHEP06(2011)001",
      year           = "2011",
      note           = "* Temporary entry *",
      eprint         = "1103.0019",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@article{Donagi:2009ra,
      author         = "Donagi, Ron and Wijnholt, Martijn",
      title          = "{Higgs Bundles and UV Completion in F-Theory}",
      year           = "2009",
      eprint         = "0904.1218",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@article{Marsano:2011hv,
      author         = "Marsano, Joseph and Schafer-Nameki, Sakura",
      title          = "{Yukawas, G-flux, and Spectral Covers from Resolved
                        Calabi-Yau's}",
      year           = "2011",
      note           = "* Temporary entry *",
      eprint         = "1108.1794",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}

@Article{KodairaII,
     author    = "Kodaira, K.",
     title     = "On compact analytic surfaces II",
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@Article{KodairaIII,
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@Article{Blumenhagen:2009yv,
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     doi       = "10.1016/j.nuclphysb.2009.12.013",
     SLACcitation  = "%%CITATION = 0908.1784;%%"
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@Article{Grimm:2009yu,
     author    = "Grimm, Thomas W. and Krause, Sven and Weigand, Timo",
     title     = "{F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds}",
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     SLACcitation  = "%%CITATION = 0912.3524;%%"
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@article{Braun:2011ux,
      author         = "Braun, Volker",
      title          = "{Toric Elliptic Fibrations and F-Theory
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      year           = "2011",
      note           = "* Temporary entry *",
      eprint         = "1110.4883",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-th",
}