论文标题
矩形的第一个Cotangent共同体学模块
The first Cotangent Cohomology Module for Matroids
论文作者
论文摘要
我们找到了一个组合公式，该公式计算与矩形相关的Stanley-Reisner环的第一个Cotangent共同体模块。对于任意的简单络合物，我们为T^1的多层组件的维度提供了上限。对于特定程度，我们证明当且仅当简单复合物是矩形时，才能达到这些边界，从而获得了矩形的新表征。此外，对无异性矩阵的完全不变的第一个cotangent共同体证明是一个完全不变的。
We find a combinatorial formula which computes the first cotangent cohomology module of Stanley-Reisner rings associated to matroids. For arbitrary simplicial complexes we provide upper bounds for the dimensions of the multigraded components of T^1. For specific degrees we prove that these bounds are reached if and only if the simplicial complex is a matroid, obtaining thus a new characterization for matroids. Furthermore, the graded first cotangent cohomology turns out to be a complete invariant for nondiscrete matroids.
