Weight systems for toric Calabi-Yau varieties and reflexivity of Newton polyhedra

Abstract

According to a recently proposed scheme for the classification of reflexive polyhedra, weight systems of a certain type play a prominent role. These weight systems are classified for the cases $n=3$ and $n=4$, corresponding to toric varieties with K3 and Calabi--Yau hypersurfaces, respectively. For $n=3$ we find the well known 95 weight systems corresponding to weighted $\IP^3$'s that allow transverse polynomials, whereas for $n=4$ there are 184026 weight systems, including the 7555 weight systems for weighted $\IP^4$'s. It is proven (without computer) that the Newton polyhedra corresponding to all of these weight systems are reflexive.

Latex, 14 pages

References in corpus (1)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

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