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Global homological mirror symmetry for genus two curves

Heather Lee, University of Washington
Tuesday, April 14, 2020 - 2:30pm
via Zoom
Heather Lee

Mirror symmetry is a duality between symplectic and complex geometries.  In her recent thesis, Cannizzo proved a homological mirror symmetry (HMS) result with the complex side being the derived category of coherent sheaves on genus two curves and the symplectic side being the Fukaya-Seidel category on the mirror (Y, W), where Y is a locally toric Calabi-Yau 3-fold and W : Y → ℂ is a symplectic fibration. Cannizzo’s thesis is for a one parameter family of complex parameters on the genus two curve. We upgrade her result to include all complex parameters and the corresponding Kahler parameters of the mirror and we identify the mirror map globally.  This is a joint work with Haniya Azam, Catherine Cannizzao, and Chiu-Chu Melissa Liu.  (I will not assume the audience knows anything about derived categories, coherent sheaves, symplectic geometry, Fukaya category, Calabi-Yau manifold, or toric manifolds.)

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