Complexes, residues and obstructions for log-symplectic manifolds

DOI10.1007/S10455-022-09881-XzbMATH Open1510.53095arXiv2103.01392MaRDI QIDQ6361884

Ziv Ran

Publication date: 1 March 2021

Abstract: We consider compact K"ahlerian 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 Poincar'e 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.

Mathematics Subject Classification ID

Calabi-Yau theory (complex-analytic aspects) (32Q25) Poisson manifolds; Poisson groupoids and algebroids (53D17) Rational and birational maps (14E05) Compact Kähler manifolds: generalizations, classification (32J27) (n)-folds ((n>4)) (14J40) Deformations of special (e.g., CR) structures (32G07)

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