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- W2962702023 abstract "We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $unicode[STIX]{x1D6F1}$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor $D(unicode[STIX]{x1D6F1})$ . We prove that $(X,unicode[STIX]{x1D6F1})$ has unobstructed deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on $H^{2}$ of the open symplectic manifold $Xsetminus D(unicode[STIX]{x1D6F1})$ , and in fact coincides with this $H^{2}$ provided the Hodge number $h_{X}^{2,0}=0$ , and finally that the degeneracy locus $D(unicode[STIX]{x1D6F1})$ deforms locally trivially under deformations of $(X,unicode[STIX]{x1D6F1})$ ." @default.
- W2962702023 created "2019-07-30" @default.
- W2962702023 creator A5006212773 @default.
- W2962702023 date "2018-11-09" @default.
- W2962702023 modified "2023-09-27" @default.
- W2962702023 title "A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION" @default.
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- W2962702023 doi "https://doi.org/10.1017/s1474748018000464" @default.
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