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Pré-Publication, Document De Travail Année : 2015

Some examples due to H. Hironaka

Daniel Barlet

Résumé

The aim of this paper is to explain the construction by H. Hironaka [H.61] of a holomorphic (in fact ''algebraic'') family of compact complex manifolds parametrized by $\C$ such for all $s \in \C\setminus \{0\}$ the fiber is projective, but such that the fiber at the origin in non k{\"a}hlerian, to mathematicians which are not algebraic geometers. We also explain why it is not possible to make in the same way such an example with fiber at $0$ a simpler example of non k{\"a}hlerian Moishezon manifold which is also due to H. Hironaka (see section 5).
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Dates et versions

hal-01100081 , version 1 (05-01-2015)
hal-01100081 , version 2 (26-03-2015)

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Daniel Barlet. Some examples due to H. Hironaka. 2015. ⟨hal-01100081v2⟩
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