Nef‐partitions arising from unimodular configurations

Abstract

AbstractReflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef‐partition of a reflexive polytope is a decomposition such that each 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.