A characterization of diagonal Poisson structures

Abstract

The degeneracy locus of a generically symplectic Poisson structure on a Fano manifold is always a singular hypersurface. We prove that there exists just one family of generically symplectic Poisson structures in Fano manifold with cyclic Picard group having a reduced simple normal crossing degeneracy locus.

16 pages

Cited by in corpus (8)

• Constructions and classifications of projective Poisson varieties
• Elliptic singularities on log symplectic manifolds and Feigin--Odesskii Poisson brackets
• Mixed Hodge structures in log symplectic geometry
• A local Torelli theorem for log symplectic manifolds
• A Bogomolov unobstructedness theorem for log-symplectic manifolds in general position
• Differential complexes and Hodge theory on log-symplectic manifolds
• An Example of Rank 2 Poisson Structure which is Stable Under Deformations
• Complexes, residues and obstructions for log-symplectic manifolds