Hilbert-Kunz multiplicity of products of ideals

TL;DR

This paper establishes bounds for the Hilbert-Kunz multiplicity of the product of two ideals and characterizes when equality holds using tight closure concepts, connecting with $*$-spread and length calculations.

Contribution

It introduces new bounds for Hilbert-Kunz multiplicity of ideal products and characterizes equality cases via tight closure, linking algebraic invariants.

Findings

Bounds for Hilbert-Kunz multiplicity of ideal products

Characterization of equality cases using tight closure

Connections with $*$-spread and length calculations

Abstract

We give bounds for the Hilbert-Kunz multiplicity of the product of two ideals, and we characterize the equality in terms of the tight closures of the ideals. Connections are drawn with $*$-spread and with ordinary length calculations.