Picard Groups of Holomorphic Poisson Manifolds
c Lie groupoid which integrates it has proven to be a powerful tool in modern Poisson geometry. A feature of the category of Lie groupoids is that the notion of morphism can be expanded to include Morita equivalences, which can be thought of as geometric bimodules. The Picard group of a Lie groupoid G is then the automorphism (2-)group of G, viewed as an object in this enlarged category. In this talk, I will describe the Picard group of a holomorphic Poisson manifold, defined to be the Picard group of its integrating holomorphic symplectic groupoid. To do this, I will demonstrate how a Morita equivalence can be described using Cech data, showing that these objects can be thought of as noncommutative line bundles.