# Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space - Mathematics > Symplectic Geometry

Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space - Mathematics > Symplectic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We introduce the notion of a tropical coamoeba which gives a combinatorialdescription of the Fukaya category of the mirror of a toric Fano stack. We showthat the polyhedral decomposition of a real n-torus into n + 1 permutohedragives a tropical coamoeba for the mirror of the projective space, and prove atorus-equivariant version of homological mirror symmetry for the projectivespace. As a corollary, we obtain homological mirror symmetry for toricorbifolds of the projective space.

Author: ** Masahiro Futaki, Kazushi Ueda**

Source: https://arxiv.org/