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

@article{Banerjee2020GeneralizedHF, title={Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex}, author={Arindam Banerjee and Kriti Goel and Jitendra Kumar Verma}, journal={arXiv: Commutative Algebra}, year={2020} }

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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