Mixed multiplicities of ideals versus mixed volumes of polytopes
By Ngô Viêt Trung, J. Verma. 2005
52 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/725980d3d909be8ca98ef8f11bede39c30ce65ef
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In Algebra and Number Theory
In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- Hilbert Functions of Filtered Modules (2007, background): “It is interesting to recall that Trung and Verma in [97] introduced superficial sequences with respect to a set of ideals by working in the multigraded contest.”
- Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs (2010, background): “Trung and Verma show in [47] that the mixed volumes of lattice polytopes in R are the mixed multiplicities of certain monomial ideals, each generated by monomials of the same degree.”