Complexes, residues and obstructions for log-symplectic manifolds

Abstract

We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic structure $\Phi$, a generically nondegenerate closed 2-form with simple poles on a divisor $D$ with local normal crossings. A simple linear inequality involving the iterated Poincaré residues of $\Phi$ at components of the double locus of $D$ ensures that the pair $(X,\Phi )$ has unobstructed deformations and that $D$ deforms locally trivially.

References in corpus (1)

• A characterization of diagonal Poisson structures