Abstract
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 \({\mathbb{P}^n}\) , and we 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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Communicated by N. A. Nekrasov
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Futaki, M., Ueda, K. Tropical Coamoeba and Torus-Equivariant Homological Mirror Symmetry for the Projective Space. Commun. Math. Phys. 332, 53–87 (2014). https://doi.org/10.1007/s00220-014-2155-1
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DOI: https://doi.org/10.1007/s00220-014-2155-1