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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.

Tropical Coamoeba and Torus-Equivariant Homological Mirror Symmetry for the Projective Space