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We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties relevant to F-theory/Heterotic duality.
Higher-dimensional toric varieties with ample anticanonical class
V. Batyrev · 1984
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N. Nakayama · 1988
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Convex bodies and algebraic geometry
T. Oda · 1988
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The number of moduli of families of curves on toric varieties, 1991
R. Koelman · 1991
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Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
V. V. Batyrev · 1994
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The homogeneous coordinate ring of a toric variety
D. A. Cox · 1995
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Symplectic cuts
E. Lerman · 1995
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Compactifications of F F -theory on Calabi-Yau threefolds. I
D. R. Morrison and C. Vafa · 1996
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Searching for K 3 K3 fibrations
A. C. Avram, M. Kreuzer, M. Mandelberg, and H. Skarke · 1997
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Toric geometry and dualities of string theory
P. Candelas · 1997
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On the classification of reflexive polyhedra
M. Kreuzer and H. Skarke · 1997
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Enhanced gauge symmetry in type II and F-theory compactifications: Dynkin diagrams from polyhedra
E. Perevalov and H. Skarke · 1997
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Heterotic string/F-theory duality from mirror symmetry
P. Berglund and P. Mayr · 1998
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Duality between the webs of heterotic and type II vacua
P. Candelas and A. Font · 1998
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Matter from toric geometry
P. Candelas, E. Perevalov, and G. Rajesh · 1998
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Principal G G -bundles over elliptic curves
R. Friedman, J. W. Morgan, and E. Witten · 1998
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Classification of reflexive polyhedra in three dimensions
M. Kreuzer and H. Skarke · 1998
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Toric geometry and F-theory/heterotic duality in four dimensions
G. Rajesh · 1998
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Toric geometry and dualities of string theory
P. Candelas · 1999
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Mirror symmetry and algebraic geometry
Positivity in algebraic geometry. I
R. Lazarsfeld · 2004
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Mathematics underlying the F-theory/heterotic string duality in eight dimensions
A. Clingher and J. W. Morgan · 2005
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Fibration structures in toric Calabi-Yau fourfolds
F. Rohsiepe · 2005
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Semistable degeneration of toric varieties and their hypersurfaces
S. Hu · 2006
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Maps of toric varieties in cox coordinates
G. Brown and J. Buczyǹski · 2010
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Background
V. Perduca · 2010
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Vector bundles over elliptic fibrations
R. Friedman, J. W. Morgan, and E. Witten · 1999
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String dualities and toric geometry: an introduction
H. Skarke · 1999
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Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
Y. Hu, C.-H. Liu, and S.-T. Yau · 2002
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Symplectic sums and Gromov-Witten invariants
E.-N. Ionel · 2002
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PALP: a package for analysing lattice polytopes with applications to toric geometry
M. Kreuzer and H. Skarke · 2004
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Toric elliptic fibrations and f-theory compactifications, 2011
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Toric varieties
D. A. Cox, J. B. Little, and H. K. Schenck · 2011
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Toric methods in f-theory model building
J. Knapp and M. Kreuzer · 2011
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Toric construction of global f-theory guts
J. Knapp, M. Kreuzer, C. Mayrhofer, and N.-O. Walliser · 2011
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Sage Mathematics Software (Version 2.7)
W. Stein et al · 2011
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Picard group of hypersurfaces in toric varieties
U. Bruzzo and A. Grassi · 2012
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