Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties

Abstract

Mirror symmetry for a toric variety involves Laurent polynomials whose symplectic topology is related to the algebraic geometry of the toric variety. We show that there is a monodromy action on the monomially admissible Fukaya-Seidel categories of these Laurent polynomials as the arguments of their coefficients vary that corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to the monomials whose coefficients are rotated. In the process, we introduce the monomially admissible Fukaya-Seidel category as a new interpretation of the Fukaya-Seidel category of a Laurent polynomial on $({\mathbb{C}}^{\ast }{)}^n$, which has other potential applications, and give evidence of homological mirror symmetry for non-compact toric varieties.

79 pages, 11 figures, comments welcome; Corrected typos and made changes to exposition

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Cited by in corpus (1)

• Moment maps, nonlinear PDE, and stability in mirror symmetry