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Gauduchons form and compactness of the space of divisors

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 نشر من قبل Daniel Barlet
 تاريخ النشر 2017
  مجال البحث
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 تأليف Daniel Barlet




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We show that in a holomorphic family of compact complex connected manifolds parametrized by an irreducible complex space $S$, assuming that on a dense Zariski open set $S^{*}$ in $S$ the fibres satisfy the $partialbarpartial-$lemma, the algebraic dimension of each fibre in this family is at least equal to the minimal algebraic dimension of the fibres in $S^{*}$. For instance, if each fibre in $S^{*}$ are Moishezon, then all fibres are Moishezon.



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