Equimultiplicity in Hilbert-Kunz theory
Commutative Algebra
2023-01-12 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1608.07600,
title = {Equimultiplicity in Hilbert-Kunz theory},
author = {Ilya Smirnov},
journal= {arXiv preprint arXiv:1608.07600},
year = {2023}
}
Comments
Update: Added a missing equidimensionality assumption in Proposition 1.22. This does not affect further results since this assumption is present therein