Convex bodies and multiplicities of ideals
Commutative Algebra
2014-02-26 v3 Algebraic Geometry
Abstract
We associate convex regions in R^n to m-primary graded sequences of subspaces, in particular m-primary graded sequences of ideals, in a large class of local algebras (including analytically irreducible local domains). These convex regions encode information about Samuel multiplicities. This is in the spirit of the theory of Grobner bases and Newton polyhedra on one hand, and the theory of Newton-Okounkov bodies for linear systems on the other hand. We use this to give a new proof, as well as a generalization of a Brunn-Minkowski inequality for multiplicities due to Teissier and Rees-Sharp.
Keywords
Cite
@article{arxiv.1302.2676,
title = {Convex bodies and multiplicities of ideals},
author = {Kiumars Kaveh and A. G. Khovanskii},
journal= {arXiv preprint arXiv:1302.2676},
year = {2014}
}
Comments
Final version, 20 pages, some typos fixed and minor corrections done. To appear in Proceedings of Steklov Institute of Mathematics