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Open Access Publications from the University of California

Monodromy of Fukaya-Seidel categories mirror to toric varieties

  • Author(s): Hanlon, Andrew
  • Advisor(s): Auroux, Denis
  • et al.

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 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 a new interpretation of the Fukaya-Seidel category of a Laurent polynomial on (C*)^n, which has other potential applications, and give evidence of homological mirror symmetry for non-compact toric varieties by computing certain Floer-theoretic natural transformations.

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