The Minkowski Equality for Filtrations
Commutative Algebra
2021-01-18 v4 Algebraic Geometry
Abstract
Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m_R. We consider multiplicities and mixed multiplicities of R by filtrations of m_R-primary ideals. We show that the theorem of Teissier, Rees and Sharp, and Katz, characterizing equality in the Minkowski inequality for multiplicities of ideals, is true for divisorial filtrations, and for the larger category of bounded filtrations. This theorem is not true for arbitrary filtrations of m_R-primary ideals.
Keywords
Cite
@article{arxiv.2007.06025,
title = {The Minkowski Equality for Filtrations},
author = {Steven Dale Cutkosky},
journal= {arXiv preprint arXiv:2007.06025},
year = {2021}
}
Comments
48 pages. This version proves the additional result (theorem 8.4) that the Minkowski equalities hold under a condition of integral dependence for arbitrary filtrations of m-primary ideals