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DEFORMATIONS FEUILLETEES DES VARIETES DE HOPF

Abstract : In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure along the non-compact leaves is fixed by the complex structure of the compact leaf. Reciprocally, we prove that the complex structure along a non-compact leaf determines the complex structure along the other leaves. We apply these results to the study of foliated deformations of Hopf manifolds, a foliated analogue to the notion of deformation in the large.
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https://hal.archives-ouvertes.fr/hal-00363022
Contributor : Laurent Meersseman Connect in order to contact the contributor
Submitted on : Friday, February 20, 2009 - 10:46:37 PM
Last modification on : Friday, November 25, 2022 - 10:12:06 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:44:02 PM

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  • HAL Id : hal-00363022, version 1
  • ARXIV : 0902.4301

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Laurent Meersseman, Marcel Nicolau, Alberto Verjovsky. DEFORMATIONS FEUILLETEES DES VARIETES DE HOPF. {date}. ⟨hal-00363022⟩

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