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

Strazzanti, Francesco; Zarzuela Armengou, Santiago

doi:10.1090/proc/15819

The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
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by Francesco Strazzanti and Santiago Zarzuela Armengou

Proc. Amer. Math. Soc. 150 (2022), 1493-1503

DOI: https://doi.org/10.1090/proc/15819

Published electronically: January 27, 2022

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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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