Coamoebas of complex algebraic plane curves and the logarithmic Gauss map

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dc.creatorNisse, Mounir
dc.date2008-05-19
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:12:53Z
dc.date.available2026-07-07T10:12:53Z
dc.descriptionThe 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 $(\mathbb{C}^*)^2$ is bounded in terms of the degree of the curve. We show in this Note that up to multiplication by a constant in $(\mathbb{C}^*)^2$, the complex algebraic plane curves whose coamoebas are of maximal area (counted with multiplicity) are defined over $\mathbb{R}$, and their real loci are Harnack curves possibly with ordinary real isolated double points (c.f. \cite{MR-00}). In addition, we characterize the complex algebraic plane curves such that their coamoebas contain no extra-piece.
dc.description11 pages, 2 figure
dc.identifierhttps://arxiv.org/abs/0805.2872
dc.identifierhttp://arxiv.org/abs/0805.2872
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172341
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.subjectComplex Variables
dc.subjectGeometric Topology
dc.titleCoamoebas of complex algebraic plane curves and the logarithmic Gauss map
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