http://arxiv.org/abs/1507.05668v1

Log symplectic manifolds are a simple class of holomorphic Poisson manifolds that have an open dense symplectic leaf, but degenerate along a hypersurface. I will explain that, subject to a natural transversality condition, the local geometry near a singular point of the hypersurface is governed by an elliptic curve. The main application is to the classification of Poisson structures on Fano fourfolds.