Equimultiplicity in Hilbert-Kunz theory

Abstract

This paper develops a theory of equimultiplicity for Hilbert-Kunz multiplicity and uses it to study the behavior of Hilbert-Kunz multiplicity on the Brenner-Monsky hypersurface. A number of applications follows, in particular we show that Hilbert-Kunz multiplicity attains infinitely many values and that equimultiple strata may not be locally closed.

Update: Added a missing equidimensionality assumption in Proposition 1.22. This does not affect further results since this assumption is present therein

References in corpus (2)

• Upper semi-continuity of the Hilbert-Kunz multiplicity
• A tight closure analogue of analytic spread

Cited by in corpus (2)

• Hilbert-Kunz multiplicity of the powers of an ideal
• Lech's conjecture in dimension three