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Complete classification of reflexive polyhedra in four dimensions

- M. Kreuzer, H. Skarke
- Physics, Mathematics
- 28 February 2000

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 in… Expand

Classification of Reflexive Polyhedra in Three Dimensions

- M. Kreuzer, H. Skarke
- Physics, Mathematics
- 27 May 1998

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 case… Expand

On the classification of quasihomogeneous functions

- M. Kreuzer, H. Skarke
- Mathematics, Physics
- 12 February 1992

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 of… Expand

PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆

- M. Kreuzer, H. Skarke
- Mathematics, Physics
- 30 April 2002

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 and… Expand

Affine Kac-Moody algebras, CHL strings and the classification of tops

- V. Bouchard, H. Skarke
- Mathematics, Physics
- 25 March 2003

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 from… Expand

Searching for K3 fibrations

- A. Avram, M. Kreuzer, M. Mandelberg, H. Skarke
- Physics, Mathematics
- 20 October 1996

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 them… Expand

NO MIRROR SYMMETRY IN LANDAU-GINZBURG SPECTRA!

- M. Kreuzer, H. Skarke
- Physics
- 2 May 1992

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 the… Expand

Calabi-Yau 4-folds and toric fibrations

- M. Kreuzer, H. Skarke
- Mathematics, Physics
- 29 January 1997

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

- P. Candelas, H. Skarke
- Physics
- 30 June 1997

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 unbroken… Expand

On the Classification of Reflexive Polyhedra

- M. Kreuzer, H. Skarke
- Mathematics, Physics
- 27 December 1995

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 with… Expand

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