论文标题
简单络合物的脸部环的REES代数的普通希尔伯特 - 昆兹功能
Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex
论文作者
论文摘要
令$ r $为尺寸$ d-1 $和$ {\ mathcal r}（\ mathfrak {n}）$的简单复合物的面环是最大均质均值$ \ mathfrak {n} $ of $ R的最大均质均值$ r的rees algebra。 r}（\ mathfrak n）/（\ mathfrak n，\ mathfrak n t）^{[s]}）$由polyenmial for a polyenmial for All $s。$我们在许多示例中计算出来，还提供了计算$ HK（S）的MACAULAY2代码。
Let $R$ be the face ring of a simplicial complex of dimension $d-1$ and ${\mathcal R}(\mathfrak{n})$ be the Rees algebra of the maximal homogeneous ideal $\mathfrak{n}$ of $R.$ We show that the generalized Hilbert-Kunz function $HK(s)=\ell({\mathcal R}(\mathfrak n)/(\mathfrak n, \mathfrak n t)^{[s]})$ is given by a polynomial for all large $s.$ We calculate it in many examples and also provide a Macaulay2 code for computing $HK(s).$
