Homological mirror symmetry for nodal stacky curves

Abstract: In this talk I will explain the proof of homological mirror symmetry where the B-side is a ring or chain of stacky projective lines joined nodally, and where each irreducible component is allowed to have a non-trivial generic stabiliser, generalising the work of Lekili and Polishchuk. The key ingredient is to match categorical resolutions on the A- and B-sides with an intermediary category given by the derived category of modules of a gentle algebra. I will begin by explaining how to construct this category from the data of the A- and B-models before moving on to applications. In particular, one can show homological mirror symmetry where the B-model is taken to be an invertible polynomial in two variables, but where the grading group is not necessarily maximal. In the maximally graded case the mirror is shown to be graded symplectomorphic to the Milnor fibre of the transpose invertible polynomial, thus establishing the Lekili-Ueda conjecture in dimension one.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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