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.