Seminar

In this thesis talk, we will describe progress towards proving homological mirror symmetry (HMS) for the genus 2 curve in an abelian variety. HMS is known for the genus 2 surface as a symplectic manifold by work of Seidel. Here we consider it on the complex manifold side. We describe a fully faithful embedding of the bounded derived category of coherent sheaves on the genus 2 curve to the Fukaya-Seidel category of a generalized SYZ mirror constructed via methods described in Abouzaid-Auroux-Katzarkov's paper on SYZ for hypersurfaces of toric varieties. HMS would be that these two categories are equivalent.