Hilbert–Kunz invariants and Euler characteristic polynomials

Larry Smith

Vol. 262 (2013), No. 1, 227–255

DOI: 10.2140/pjm.2013.262.227

Abstract

We study the Hilbert–Kunz invariants of homogeneous ideals in graded polynomial algebras and develop a homological formula for the Hilbert–Kunz multiplicity resembling the formula of J.-P.  Serre using Koszul homology for the ordinary multiplicity of an ideal. We apply this in the special case of maximal primary irreducible ideals to obtain several new results, among which is a reciprocity formula for the Hilbert–Kunz invariants of directly linked ideals in a graded polynomial algebra.

Keywords

Hilbert–Kunz invariants, linkage of ideals

Mathematical Subject Classification 2010

Primary: 13A15, 13D02, 18G00

Milestones

Received: 1 December 2011

Revised: 26 December 2012

Accepted: 27 December 2012

Published: 27 March 2013