Gorenstein polytopes with trinomial h*-polynomials
Gorenstein polytopes with trinomial h*-polynomials
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具有三项式 h* 多项式的 Gorenstein 多面体
DOI：
10.1007/s13366-020-00513-8
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Benjamin Nill and Akiyoshi Tsuchiya
中科院分区：
文献类型：
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作者：
Akihiro Higashitani;Benjamin Nill and Akiyoshi Tsuchiya
基于晶格多面体ehrhart多项式信息的表征是一个困难的开放问题。本文完成了晶格多面体的分类，其多项式满足两个性质：它们是回文的（因此多面体是戈伦斯坦的），并且它们恰好由三个项组成。这扩展了由Batyrev和Juny提出的二阶Gorenstein多面体的分类。这个证明依赖于Batyrev和Hofscheier最近对多项式恰好有两项的空格简式的描述。从我们的定理的角度来看，我们总结了这些结果和该领域的其他现有结果。
The characterization of lattice polytopes based upon information about their Ehrhart-polynomials is a difficult open problem. In this paper, we finish the classification of lattice polytopes whose-polynomials satisfy two properties: they are palindromic (so the polytope is Gorenstein) and they consist of precisely three terms. This extends the classification of Gorenstein polytopes of degree two due to Batyrev and Juny. The proof relies on the recent characterization of Batyrev and Hofscheier of empty lattice simplices whose-polynomials have precisely two terms. Putting our theorem in perspective, we give a summary of these and other existing results in this area.