Poisson modules and degeneracy loci (Q2848492)

This paper studies the link between Poisson modules and other sub-objects in holomorphic Poisson geometry. The authors start with some recalls about Poisson geometry and Poisson modules. Then they define the residues of a Poisson line bundle and introduce the notion of degeneracy loci of a Poisson module. These notions enable them to explain how the degeneracy loci can be used to obtain Bott-type vanishing theorems for Poisson modules. In particular, the authors find formulae for the residues in terms of the Poisson tensor. The results are also applied to a family of Poisson structures defined by Felgin and Odesski, related to elliptic normal curves.