摘要翻译：
我们建立了超曲面簇的orbifold上同调与Lawrence多边形的Ehrhart理论之间的联系。更具体地说，我们证明了超曲面簇的orbifold上同调群的维数等于相关Lawrence多面体的Ehrhart$delta$-多项式的系数。由此，我们导出了Lawrence多面体的Ehrhart$Delta$-多项式的一个公式，并利用超曲面类的Hard Lefschetz定理的内射部分导出了该多项式系数之间的一些不等式。
---
英文标题：
《Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of
  Hypertoric Varieties》
---
作者：
Alan Stapledon
---
最新提交年份：
2008
---
分类信息：

一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
--
一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
英文摘要：
  We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are equal to the coefficients of the Ehrhart $\delta$-polynomial of the associated Lawrence polytope. As a consequence, we deduce a formula for the Ehrhart $\delta$-polynomial of a Lawrence polytope and use the injective part of the Hard Lefschetz Theorem for hypertoric varieties to deduce some inequalities between the coefficients of the $\delta$-polynomial.
---
PDF链接：
https://arxiv.org/pdf/0806.4669