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Jorge Pereira will speak on

A global Weinstein splitting theorem for holomorphic Poisson manifolds

Abstract:Any Poisson bracket on a differentiable manifold can be written locally as the sum of two commuting Poisson brackets: a Poisson bracket of symplectic form and a Poisson bracket that vanishes at a point. This is the so-called Weinstein splitting. The result is strictly local; in general, it is impossible to globalize the two local Poisson structures. It turns out that for holomorphic Poisson structures on compact Kähler manifolds admitting a simply-connected compact symplectic leaf, the local Weinstein splitting globalizes and produces a global splitting of a finite étale cover of the ambient manifold as a product of two compact Kähler Poisson manifolds. Based on, a joint work with Stéphane Druel, Jorge Vitório Pereira, and Frédéric Touzet.