Built on

K. Kodaira, “On compact analytic surfaces II,” Ann. M
1963
Earlier work this paper cites.
Springer, Berlin/Heidelberg, 1975
J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil · 1975
Earlier work this paper cites.
V. V. Batyrev and L. A. Borisov, “Mirror duality and string-theoretic Hodge numbers,” Invent. Math
1983
Earlier work this paper cites.
T. Oda and H. Park, “Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions,” Tôhoku Math. J
1991
Earlier work this paper cites.
Princeton University Press, 1993
W. Fulton, Introduction to Toric Varieties · 1993
Earlier work this paper cites.
Wiley Classics Library. John Wiley & Sons Ltd., New York, NY, 1994
P. Griffiths and J. Harris, Principles of algebraic geometry · 1994
Earlier work this paper cites.
V. V. Batyrev, “Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties,” J. Alg. Geom
1994
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P. Berglund, S. H. Katz, and A. Klemm, “Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties,” Nucl.Phys
1995
Earlier work this paper cites.
C. Vafa, “Evidence for F-Theory,” Nucl. Phys
1996
Earlier work this paper cites.
Amer. Math. Soc., Providence, RI, 1997
V. V. Batyrev and L. A. Borisov, “Dual cones and mirror symmetry for generalized Calabi-Yau manifolds,” in Mirror symmetry, II · 1997
Earlier work this paper cites.
World Scientific, 2002
J. Rambau, “TOPCOM: Triangulations of point configurations and oriented matroids,” in Mathematical Software—ICMS 2002 · 2002
Earlier work this paper cites.
M. Kreuzer and H. Skarke, “Complete classification of reflexive polyhedra in four dimensions,” Adv. Theor. Math. Phys
2002
Earlier work this paper cites.
M. Kreuzer and H. Skarke, “PALP: A Package for analyzing lattice polytopes with applications to toric geometry,” Comput. Phys. Commun
2004
Earlier work this paper cites.
C. Beasley, J. J. Heckman, and C. Vafa, “GUTs and Exceptional Branes in F-theory - I,” JHEP
Original
2009
Earlier work this paper cites.

Similar

C. Beasley, J. J. Heckman, and C. Vafa, “GUTs and Exceptional Branes in F-theory - II: Experimental Predictions,” JHEP
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Original

Then

J. J. Heckman, Y. Tachikawa, C. Vafa, and B. Wecht, “N = 1 SCFTs from Brane Monodromy,” JHEP
Original
2010
Later among the works it cites.
A. Collinucci, “New F-theory lifts. II. Permutation orientifolds and enhanced singularities,” JHEP
Original
2010
Later among the works it cites.
J. J. Heckman, “Particle Physics Implications of F-theory,” Ann.Rev.Nucl.Part.Sci
Original
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Later among the works it cites.
T. Weigand, “Lectures on F-theory compactifications and model building,” Class. Quant. Grav
Original
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Later among the works it cites.
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Later among the works it cites.

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2011

Toric Methods in F-theory Model Building

Knapp, Johanna, Kreuzer, Maximilian

Understand

In this review article we discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework.

After introducing the basic properties of global F-theory GUTs we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models.
We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.

Built on

K. Kodaira, “On compact analytic surfaces II,” Ann. M
1963
Earlier work this paper cites.
Springer, Berlin/Heidelberg, 1975
J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil · 1975
Earlier work this paper cites.
V. V. Batyrev and L. A. Borisov, “Mirror duality and string-theoretic Hodge numbers,” Invent. Math
1983
Earlier work this paper cites.
T. Oda and H. Park, “Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions,” Tôhoku Math. J
1991
Earlier work this paper cites.
Princeton University Press, 1993
W. Fulton, Introduction to Toric Varieties · 1993
Earlier work this paper cites.
Wiley Classics Library. John Wiley & Sons Ltd., New York, NY, 1994
P. Griffiths and J. Harris, Principles of algebraic geometry · 1994
Earlier work this paper cites.
V. V. Batyrev, “Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties,” J. Alg. Geom
1994
Earlier work this paper cites.
P. Berglund, S. H. Katz, and A. Klemm, “Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties,” Nucl.Phys
1995
Earlier work this paper cites.
C. Vafa, “Evidence for F-Theory,” Nucl. Phys
1996
Earlier work this paper cites.
Amer. Math. Soc., Providence, RI, 1997
V. V. Batyrev and L. A. Borisov, “Dual cones and mirror symmetry for generalized Calabi-Yau manifolds,” in Mirror symmetry, II · 1997
Earlier work this paper cites.
World Scientific, 2002
J. Rambau, “TOPCOM: Triangulations of point configurations and oriented matroids,” in Mathematical Software—ICMS 2002 · 2002
Earlier work this paper cites.
M. Kreuzer and H. Skarke, “Complete classification of reflexive polyhedra in four dimensions,” Adv. Theor. Math. Phys
2002
Earlier work this paper cites.
M. Kreuzer and H. Skarke, “PALP: A Package for analyzing lattice polytopes with applications to toric geometry,” Comput. Phys. Commun
2004
Earlier work this paper cites.
C. Beasley, J. J. Heckman, and C. Vafa, “GUTs and Exceptional Branes in F-theory - I,” JHEP
Original
2009
Earlier work this paper cites.

Similar

C. Beasley, J. J. Heckman, and C. Vafa, “GUTs and Exceptional Branes in F-theory - II: Experimental Predictions,” JHEP
Original
2009
Cited alongside, same era.
A. Collinucci, “New F-theory lifts,” JHEP
Original
2009
Cited alongside, same era.
R. Blumenhagen, T. W. Grimm, B. Jurke, and T. Weigand, “F-theory uplifts and GUTs,” JHEP
Original
2009
Cited alongside, same era.
M. Kreuzer, “The Making of Calabi-Yau spaces: Beyond toric hypersurfaces,” Fortsch.Phys
Original
2009
Cited alongside, same era.
A. Collinucci, M. Kreuzer, C. Mayrhofer, and N.-O. Walliser, “Four-modulus ’Swiss Cheese’ chiral models,” JHEP
Original

Then

J. J. Heckman, Y. Tachikawa, C. Vafa, and B. Wecht, “N = 1 SCFTs from Brane Monodromy,” JHEP
Original
2010
Later among the works it cites.
A. Collinucci, “New F-theory lifts. II. Permutation orientifolds and enhanced singularities,” JHEP
Original
2010
Later among the works it cites.
J. J. Heckman, “Particle Physics Implications of F-theory,” Ann.Rev.Nucl.Part.Sci
Original
2010
Later among the works it cites.
T. Weigand, “Lectures on F-theory compactifications and model building,” Class. Quant. Grav
Original
2010
Later among the works it cites.
M. Kreuzer, “Toric Geometry and Calabi-Yau Compactifications,” Ukr. J. Phys
2010
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2009

Cited alongside, same era.

B. Andreas and G. Curio, “From Local to Global in F-Theory Model Building,” J.Geom.Phys

Original

2010

Cited alongside, same era.

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Original

2010

Cited alongside, same era.

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Original

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Cited alongside, same era.

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Original

2010

Cited alongside, same era.

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Original

2010

Cited alongside, same era.

H. Hayashi, T. Kawano, Y. Tsuchiya, and T. Watari, “More on Dimension-4 Proton Decay Problem in F-theory – Spectral Surface, Discriminant Locus and Monodromy,” Nucl. Phys

Original

2010

Cited alongside, same era.

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2010

Cited alongside, same era.

R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy, “Cohomology of Line Bundles: A Computational Algorithm,” J. Math. Phys

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Later among the works it cites.

M. Cvetic, I. Garcia-Etxebarria, and J. Halverson, “Global F-theory Models: Instantons and Gauge Dynamics,” JHEP

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2011

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Original

2011

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Y.-C. Chung, “On Global Flipped SU(5) GUTs in F-theory,” JHEP

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J. Marsano, “Hypercharge Flux, Exotics, and Anomaly Cancellation in F-theory GUTs,” Phys.Rev.Lett

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D. A. Cox, J. B. Little, and H. Schenck, “Toric Varieties.” to be published by AMS in 2011, currently available at: http://www.cs.amherst.edu/~dac/toric.html

2011

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2011

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