Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space

Details Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space

2010-01-27

arxiv.org/abs/1001.4858v2

Mathematics

Symplectic Geometry

30 pages, 29 figures; v2: typos corrected and minor changes here and there

Scientific paper

We introduce the notion of a tropical coamoeba which gives a combinatorial description of the Fukaya category of the mirror of a toric Fano stack. We show that the polyhedral decomposition of a real n-torus into (n + 1) permutohedra gives a tropical coamoeba for the mirror of the projective space, and prove a torus-equivariant version of homological mirror symmetry for the projective space. As a corollary, we obtain homological mirror symmetry for toric orbifolds of the projective space.

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