On mixed multiplicities of ideals
Abstract
Let R be the local ring of a point on a variety X over an algebraically closed field k. We make a connection between the notion of mixed (Samuel) multiplicity of m-primary ideals in R and intersection theory of subspaces of rational functions on X which deals with the number of solutions of systems of equations. From this we readily deduce several properties of mixed multiplicities. In particular, we prove a (reverse) Alexandrov-Fenchel inequality for mixed multiplicities due to Teissier and Rees-Sharp. As an application in convex geometry we obtain a proof of a (reverse) Alexandrov-Fenchel inequality for covolumes of convex bodies inscribed in a convex cone.
Keywords
Cite
@article{arxiv.1310.7979,
title = {On mixed multiplicities of ideals},
author = {Kiumars Kaveh and A. G. Khovanskii},
journal= {arXiv preprint arXiv:1310.7979},
year = {2015}
}
Comments
Minor corrections: a reference to a paper of B. Teissier added and reference to results of B. Teissier and Rees-Sharp in the introduction corrected