Coamoebas of Complex Algebraic Plane Curves and the Logarithmic Gauss Map
نویسنده
چکیده
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 de ned over R, and their real loci are Harnack curves possibly with ordinary real isolated double points (c.f. [MR-00]). In addition, we characterize the complex algebraic plane curves such that their coamoebas contain no extra-piece.
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