Homological mirror symmetry for a complex genus 2 curve

Homological mirror symmetry for a complex genus 2 curve

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Catherine Canizzo, Stony Brook University
Fine Hall 224

We will discuss work from https://arxiv.org/abs/1908.04227 on a homological mirror symmetry result for a complex genus 2 curve. We will first note how the result fits into the broader framework of HMS examples. Then we will describe the geometric construction of the mirror. Finally we will see the algebraic result on homogenous coordinate rings, i.e. the HMS result on the level of cohomology. The method involves first considering mirror symmetry for the 4-torus, then extending to a correspondence between a hypersurface genus 2 curve and a mirror Landau-Ginzburg model with fiber the mirror 4-torus. This is work from my thesis under my advisor Professor Denis Auroux.