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

Abstract

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 $HK(s).$

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