2008/12/26 by Kiumars Kaveh, Kaveh, Kiumars, Askold Khovanskiĭ +1 · 2 citations
Computer Science · Mathematics · #14C20 #52A39 #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0812.4688
openalex publication_date 2008/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theorem to generic systems of algebraic equations on any quasi-projective variety. In the present note we review these results and their applications to algebraic geometry and convex geometry.