Corpus ID: 211817918

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}
}
  • Arindam Banerjee, Kriti Goel, Jitendra Kumar Verma
  • Published 2020
  • Mathematics
  • arXiv: Commutative Algebra
  • 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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