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.