Shifted Poisson structure and elliptic deformation

Abstract

There are two sources of examples of high dimensional Poisson varieties in algebraic geometry. The first class appears as moduli space of sheaves on Poisson surface (due to Mukai and Bottacin). The second class comes from finite dimensional pieces 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 some nice description for the symplectic leaves of these Poisson structures. This is a joint work with Alexander Polishchuk.