%0 Journal Article
%T On mixed multiplicities of ideals
%A Kiumars Kaveh
%A A. G. Khovanskii
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1310.7979v2