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A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION

  • Ziv Ran (a1)

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 $X\setminus D(\unicode[STIX]{x1D6F1})$ , 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 $(X,\unicode[STIX]{x1D6F1})$ .

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A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION

  • Ziv Ran (a1)

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