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Complete classification of reflexive polyhedra in four dimensions
Four dimensional reflexive polyhedra encode the data for smooth Calabi-Yau threefolds that are hypersurfaces in toric varieties, and have important applications both in perturbative and inExpand
Classification of Reflexive Polyhedra in Three Dimensions
We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the caseExpand
On the classification of quasihomogeneous functions
We give a criterion for the existence of a non-degenerated quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation ofExpand
PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex andExpand
Affine Kac-Moody algebras, CHL strings and the classification of tops
Candelas and Font introduced the notion of a `top' as half of a three dimensional reflexive polytope and noticed that Dynkin diagrams of enhanced gauge groups in string theory can be read off fromExpand
Searching for K3 fibrations
Abstract We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyze 184 026 such spaces and identify among themExpand
We use a recent classification of non-degenerate quasihomogeneous polynomials to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field theories with c=9 and calculate theExpand
Calabi-Yau 4-folds and toric fibrations
Abstract We present a general scheme for identifying fibrations in the framework of toric geometry and provide a large list of weights for Calabi-Yau 4-folds. We find 914 164 weights with degree d ≤Expand
F-theory, SO(32) and Toric Geometry
Abstract We show that the F-theory dual of the heterotic string with unbroken Spin(32)/ Z 2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbrokenExpand
On the Classification of Reflexive Polyhedra
Abstract: Reflexive polyhedra encode the combinatorial data for mirror pairs of Calabi–Yau hypersurfaces in toric varieties. We investigate the geometrical structures of circumscribed polytopes withExpand