2008/05/19 by Mounir Nisse, Nisse, Mounir · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0805.2872
openalex publication_date 2008/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The coamoeba of any complex algebraic plane curve V is its image in the real torus under the argument map. The area counted with multiplicity of the coamoeba of any algebraic curve in (ℂ^*)2 is bounded in terms of the degree of the curve. We show in this Note that up to multiplication by a constant in (ℂ^*)2, the complex algebraic plane curves whose coamoebas are of maximal area (counted with multiplicity) are defined over ℝ, and their real loci are Harnack curves possibly with ordinary real isolated double points (c.f. \citeMR-00). In addition, we characterize the complex algebraic plane curves such that their coamoebas contain no extra-piece.