非正规仿射幺半群
Non-normal affine monoids
摘要：
给出了非正规仿射幺半群$Q$中洞集的几何描述。这组洞与$k[Q]$的局部上同调的非平凡分次分量有关。由此，我们看到$k[Q]$的各种属性，如局部正规性和塞尔条件$(R_1)$和$(S_2)$是如何在孔的几何形状中编码的。给出了么半群代数$k[Q]$深度的一个组合上界，并指出了等式成立的一些情况。我们将这一结果应用到正规仿射幺半群。
英文摘要：
We give a geometric description of the set of holes in a non-normal affine monoid $Q$. The set of holes turns out to be related to the non-trivial graded components of the local cohomology of $k[Q]$. From this, we see how various properties of $k[Q]$ like local normality and Serre's conditions $(R_1)$ and $(S_2)$ are encoded in the geometry of the holes. A combinatorial upper bound for the depth the monoid algebra $k[Q]$ is obtained and some cases where equality holds are identified. We apply this results to seminormal affine monoids.
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