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- Title
A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION.
- Authors
Ran, Ziv
- Abstract
We consider compact Kählerian manifolds X of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure Π which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor D(Π). We prove that (X,Π) has unobstructed deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on H2 of the open symplectic manifold X \ D(Π), and in fact coincides with this H2 provided the Hodge number hX2,0 = 0, and finally that the degeneracy locus D(Π) deforms locally trivially under deformations of (X,Π).
- Publication
Journal of the Institute of Mathematics of Jussieu, 2020, Vol 19, Issue 5, p1509
- ISSN
1474-7480
- Publication type
Article
- DOI
10.1017/S1474748018000464