Shifted poisson structure and moduli space of complexes

Abstract

There are two sources of examples of high dimensional Poisson varieties in algebraic geometry. The first class of examples appear as moduli spaces of sheaves on Poisson surface (whose Poisson structure is constructed by Mukai and Bottacin). The second class comes from finite dimensional sub varieties of loop algebras. with Poisson structure given by solutions of classical Yang-Baxter equation. In this talk, I will explain how these two very different constructions can be unified via Shifted Poisson structure (defined by Calaque-Pantev-Toen-Vaquie-Vezzosi). As an application, we obtain classification of the symplectic leaves for a large class of Poisson structures associated to elliptic curves. This is a joint work with Alexander Polishchuk.