Amoeba finite basis of solutions to a system of n polynomials in n\n variables

2014/04/14 by Mounir Nisse, Nisse, Mounir
Computer Science · Mathematics · #14T05 #32A60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Mathematical and Theoretical Analysis #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1404.3593

openalex publication_date 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the amoeba of a complex algebraic variety defined as the\nsolutions to a generic system of n polynomials in n variables has a finite\nbasis. In other words, it is the intersection of finitely many hypersurface\namoebas. Moreover, we give an upper bound of the size of the basis in terms of\nn and the mixed volume \μ of the Newton polytopes of the polynomial\nequations of the system. Also, we give an upper bound of the degree of the\nbasis elements in terms of \μ.\n

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