Complex tropical localization, coamoebas, and mirror tropical hypersurfaces

Details Complex tropical localization, coamoebas, and mirror tropical hypersurfaces Complex tropical localization, coamoebas, and mirror tropical hypersurfaces

2008-06-11

arxiv.org/abs/0806.1959v1

Mathematics

Algebraic Geometry

20 pages, 24 figures

Scientific paper

We introduce in this paper the concept of tropical mirror hypersurfaces and we prove a complex tropical localization Theorem which is a version of Kapranov's Theorem \cite{K-00} in tropical geometry. We give a geometric and a topological equivalence between coamoebas of complex algebraic hypersurfaces defined by a maximally sparse polynomial and coamoebas of maximally sparse complex tropical hypersurfaces.

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