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Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications

2008/02/17 by Ngô Viêt Trung, N. V. Trung, Trung, N. V. +2
Computer Science · Mathematics · #13H15 52B20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #math.AG #msc:13H15 #msc:52B20

paper · pdf · doi:10.48550/arxiv.0802.2329

34 pages

arxiv created 2008/02/17 · openalex publication_date 2008/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicities of blowup algebras and mixed volumes of polytopes.

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