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arXiv · 1809.06001

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

Andrew Hanlon
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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 $(\mathbb{C}^*)^n$, which has other potential applications, and give evidence of homological mirror symmetry for non-compact toric varieties.

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Andrew Hanlon. 2018-09-17. Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties. https://arxiv.org/abs/1809.06001

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