Mixed multiplicities of ideals versus mixed volumes of polytopes
Abstract
Description
The main results of this paper interpret mixed volumes of lattice polytopes as mixed multiplicities of ideals and mixed multiplicities of ideals as Samuel's multiplicities. In particular, we can give a purely algebraic proof of Bernstein's theorem which asserts that the number of common zeros of a system of Laurent polynomial equations in the torus is bounded above by the mixed volume of their Newton polytopes.
19 pages, to appear in Trans. Amer. Math. Soc
19 pages, to appear in Trans. Amer. Math. Soc