Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces

Abstract

We formulate a conjecture which describes the Fukaya category of an exact Lefschetz fibration defined by a Laurent polynomial in two variables in terms of a pair consisting of a consistent dimer model and a perfect matching on it. We prove this conjecture in some cases, and obtain homological mirror symmetry for quotient stacks of toric del Pezzo surfaces by finite subgroups of the torus as a corollary.

arXiv comment23 pages, 40 figures; v2:completely rewritten; v3:Incorporated suggestions by the referee

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• A Dimer ABC
• Tropical mirror symmetry for elliptic curves
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• Homological mirror symmetry for local Calabi-Yau manifolds via SYZ