论文标题
薄层：带有消失的本地$ h^*$ - 多项式的晶格多面有
Thin polytopes: Lattice polytopes with vanishing local $h^*$-polynomial
论文作者
论文摘要
在本文中，我们研究了薄型多型的新颖概念：晶格多塔的局部$ h^*$ - 多项式消失。本地$ H^*$ - 多项式是现代Ehrhart理论中的重要不变。它的定义可以追溯到斯坦利（Stanley），卡鲁（Karu），鲍里索夫（Borisov）和马维洛托夫（Mavlyutov），施佩斯（Schepers）和卡兹（Katz＆Stapledon）取得了基本结果。对薄简便的研究最初是由Gelfand，Kapranov和Zelevinsky提出的，在这种情况下，在这种情况下，局部$ H^*$ - 多项式简单地等于其所谓的盒子多项式。我们的主要结果是将薄的多面体的完整分类至尺寸3，以及戈伦斯坦多型的薄度的表征。该论文还包括对本地$ H^*$ - 多项式的简介，并对先前的结果进行了调查。
In this paper we study the novel notion of thin polytopes: lattice polytopes whose local $h^*$-polynomials vanish. The local $h^*$-polynomial is an important invariant in modern Ehrhart theory. Its definition goes back to Stanley with fundamental results achieved by Karu, Borisov & Mavlyutov, Schepers, and Katz & Stapledon. The study of thin simplices was originally proposed by Gelfand, Kapranov and Zelevinsky, where in this case the local $h^*$-polynomial simply equals its so-called box polynomial. Our main results are the complete classification of thin polytopes up to dimension 3 and the characterization of thinness for Gorenstein polytopes. The paper also includes an introduction to the local $h^*$-polynomial with a survey of previous results.
