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arXiv · 2002.00282

The Hilbert-Kunz function of some quadratic quotients of the Rees algebra

Francesco Strazzanti·Santiago Zarzuela Armengou
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Abstract

Given a commutative local ring $(R,\mathfrak m)$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[It]$ has been recently studied as a unified approach to the Nagata's idealization and the amalgamated duplication and as a way to construct interesting examples, especially integral domains. When $R$ is noetherian of prime characteristic, we compute the Hilbert-Kunz function of the members of this family and, provided that either $I$ is $\mathfrak{m}$-primary or $R$ is regular and F-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored.

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Francesco Strazzanti, Santiago Zarzuela Armengou. 2020-02-01. The Hilbert-Kunz function of some quadratic quotients of the Rees algebra. https://arxiv.org/abs/2002.00282

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