二木 昌宏

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 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.

We prove homological mirror symmetry for Lefschetz fibrations obtained as Sebastiani-Thom sums of polynomials of types A or D. The proof is based on the behavior of the Fukaya category under Sebastiani-Thom summation of a polynomial of type D. © 2012 Springer-Verlag.