Analytic varieties with finite volume amoebas are algebraic

2011/08/06 by Farid Madani, Mounir Nisse, Madani, Farid +1
Computer Science · Mathematics · #14T05 #32A60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1108.1444

openalex publication_date 2011/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the amoeba volume of a given k-dimensional generic analytic variety V of the complex algebraic torus (\C^*)ⁿ. When n≥ 2k, we show that V is algebraic if and only if the volume of its amoeba is finite. In this precise case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the k-linear spaces will be given.

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