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ERRATUM/CORRIGENDUM, OCTOBER 2020, FOR ’A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION’ (J. INST. MATH. JUSSIEU 19 (2018), 1509–1519)
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- Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 1 / January 2023
- Published online by Cambridge University Press:
- 16 April 2021, pp. 275-277
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- January 2023
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A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 5 / September 2020
- Published online by Cambridge University Press:
- 09 November 2018, pp. 1509-1519
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- September 2020
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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 
$(X,\unicode[STIX]{x1D6F1})$.
