Nef-partitions arising from unimodular configurations

Abstract

Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef-partition of a reflexive polytope $\mathcal{P}$ is a decomposition $\mathcal{P}={\mathcal{P}}_1+\cdots +{\mathcal{P}}_r$ such that each ${\mathcal{P}}_i$ is a lattice polytope containing the origin. Batyrev and van Straten gave a combinatorial method for explicit constructions of mirror pairs of Calabi-Yau complete intersections obtained from nef-partitions. In the present paper, by means of Gröbner basis techniques, we give a large family of nef-partitions arising from unimodular configurations.

12 pages, typos are corrected, the writing is improved