Regular Unimodular Triangulations of Reflexive IDP 2-Supported Weighted Projective Space Simplices
Regular Unimodular Triangulations of Reflexive IDP 2-Supported Weighted Projective Space Simplices
复制标题
DOI：
10.1007/s00026-021-00554-3
复制
发表时间：
2021-09
影响因子：
0.5
通讯作者：
Benjamin Braun;Derek Hanely
中科院分区：
文献类型：
--
作者：
Benjamin Braun;Derek Hanely
对于每个具有 d 个部分的整数分区，我们用作为标准基向量中的凸包获得的格子单纯形以及向量来表示。对于两个不同的部分，例如自反性且具有整数分解性质，我们建立了其中包含的格点的表征。然后，我们使用由这些单纯形定义的环面理想的无平方初始理想构造一个 Gröbner 基。这证明了具有整数分解性质的自反 2-支持的正则单模三角剖分的存在性。作为推论，我们获得了这些单纯形具有单峰 Ehrhart 向量的新证明。
For each integer partitionwithdparts, we denote bythe lattice simplex obtained as the convex hull inof the standard basis vectors along with the vector. Forwith two distinct parts such thatis reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in. We then construct a Gröbner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular unimodular triangulation for reflexive 2-supportedhaving the integer decomposition property. As a corollary, we obtain a new proof that these simplices have unimodal Ehrhart-vectors.