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

Arindam Banerjee; Kriti Goel; J. K. Verma

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

Commutative Algebra 2021-03-02 v2

Authors: Arindam Banerjee , Kriti Goel , J. K. Verma

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 $HK(s).$

Keywords

hilbert-kunz function rees algebra face ring simplicial complex macaulay2

Cite

@article{arxiv.2003.01438,
  title  = {Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex},
  author = {Arindam Banerjee and Kriti Goel and J. K. Verma},
  journal= {arXiv preprint arXiv:2003.01438},
  year   = {2021}
}

Comments

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

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

Abstract

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