# Nef-partitions arising from unimodular configurations

## TL;DR

This paper introduces a new method for constructing nef-partitions of reflexive polytopes using Gröbner basis techniques, expanding the class of known nef-partitions from unimodular configurations.

## Contribution

It provides a large family of nef-partitions derived from unimodular configurations through Gröbner basis methods, enhancing combinatorial and algebraic tools for mirror symmetry.

## Key findings

- Constructed numerous nef-partitions from unimodular configurations.
- Applied Gröbner basis techniques to combinatorial geometry.
- Extended the class of nef-partitions available for mirror symmetry studies.

## 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 Gr\"{o}bner basis techniques, we give a large family of nef-partitions arising from unimodular configurations.