论文标题
在矩阵多面体的代数特性上
On algebraic properties of matroid polytopes
论文作者
论文摘要
复曲面的品种是由晶格多层构造的。在代数组合学中，通常将代数性质从多种多样到多层植物的概念携带。从组合的角度来看，圆环品种的最有趣的结构之一来自矩阵的基础多层。矩阵碱基多面体和独立性多面是cohen--macaulay。我们研究了两个天然强大的代数特性 - 戈伦斯坦和光滑。我们提供了完整的矩形分类，其独立性多层或基础多层是光滑的或戈伦斯坦的。后者回答了Herzog和Hibi提出的一个问题。
A toric variety is constructed from a lattice polytope. It is common in algebraic combinatorics to carry this way a notion of an algebraic property from the variety to the polytope. From the combinatorial point of view, one of the most interesting constructions of toric varieties comes from the base polytope of a matroid. Matroid base polytopes and independence polytopes are Cohen--Macaulay. We study two natural stronger algebraic properties -- Gorenstein and smooth. We provide a full classifications of matroids whose independence polytope or base polytope is smooth or Gorenstein. The latter answers to a question raised by Herzog and Hibi.
