Mixed multiplicities of ideals versus mixed volumes of polytopes

• Autores: Ngo Viet Trung, Jugal Verma
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 10, 2007, págs. 4711-4727
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04054-8
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• Resumen

  • 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.