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

Abstract

Given a commutative local ring ( R , m ) (R,\mathfrak m) and an ideal I I of R R , a family of quotients of the Rees algebra R [ I t ] 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 R is noetherian of prime characteristic, we compute the Hilbert-Kunz function of the members of this family and, provided that either I I is m \mathfrak {m} -primary or R R is regular and F-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored.