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arXiv 2003.014382020-03math.AC

Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex

Arindam Banerjee, Kriti Goel, J. K. Verma

备注：: to appear in Commutative Algebra:150 years with Roger and Sylvia Wiegand, Contemporary Mathematics, Amer. Math. Soc

英文摘要：

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 $HK(s).$

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