Mixed multiplicities of ideals versus mixed volumes of polytopes

Ngo Viet Trung; Jugal Verma

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Mixed multiplicities of ideals versus mixed volumes of polytopes

Ngo Viet Trung·Jugal Verma

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Abstract

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.

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Ngo Viet Trung, Jugal Verma. 2005-04-08. Mixed multiplicities of ideals versus mixed volumes of polytopes. https://arxiv.org/abs/math/0504178

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