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 using the algebraic technique on Grobner bases, we give a large family of nef-partitions arising from unimodular configurations.

中文翻译：

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由单模配置引起的 Nef 分区

已经从组合学、交换代数和代数几何的角度研究了自反多胞体。自反多胞体 $\mathcal{P}$ 的 nef 分区是分解 $\mathcal{P}=\mathcal{P}_1+\cdots+\mathcal{P}_r$ 使得每个 $\mathcal{P}_i $ 是包含原点的晶格多面体。Batyrev 和 van Straten 给出了从 nef 分区获得的 Calabi-Yau 完全交叉的镜像对的显式构造的组合方法。在本文中，通过在 Grobner 基上使用代数技术，我们给出了由单模配置产生的一大类 nef 分区。