Global homological mirror symmetry for genus 2 curves

Abstract: A smooth genus 2 curve has a 6 dimensional family of possible complex structures, parametrized by the genus-2 Siegel space. We describe a generalized SYZ mirror family of symplectic manifolds, and the mirror correspondence of Kähler cones with the Siegel space. We also describe the Fukaya category of the symplectic manifold (a Landau-Ginzburg model), with structure maps deformed by the B-field. This involves adapting Guillemin’s Kähler potential to a toric variety of infinite type and computing monodromy of a symplectic fibration with critical locus given by the “banana manifold” of three P^1’s attached at two points. Finally, we end with a homological mirror symmetry result between the genus 2 curves and their mirrors. This is joint work with H. Azam, C-C. M. Liu, and H. Lee.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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