Comptes Rendus
no. 3-4
Complex Analysis
Oka maps
[Les applications d'Oka]

Présenté par : Mikhaël Gromov

Franc Forstnerič1
1 Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 145-148.

Nous prouvons que, pour une submersion holomorphe des espaces complexes réduits, la propriété d'Oka simple implique la propriété d'Oka paramétrique. En particulier, toute submersion sous-elliptique stratifié possède la propriété d'Oka paramétrique.

We prove that for a holomorphic submersion of reduced complex spaces, the basic Oka property implies the parametric Oka property. It follows that a stratified subelliptic submersion, or a stratified fiber bundle whose fibers are Oka manifolds, enjoys the parametric Oka property.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.12.004
Franc Forstnerič 1

1 Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia 
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Franc Forstnerič. Oka maps. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 145-148. doi : 10.1016/j.crma.2009.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.004/

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[6] F. Forstnerič; E.F. Wold Fibrations and Stein neighborhoods (Proc. Amer. Math. Soc., in press) | arXiv

[7] M. Gromov Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc., Volume 2 (1989), pp. 851-897

[8] B. Ivarsson; F. Kutzschebauch A solution of Gromov's Vaserstein problem, C. R. Acad. Sci. Paris Ser. I, Volume 346 (2008), pp. 1239-1243

[9] F. Lárusson Model structures and the Oka principle, J. Pure Appl. Algebra, Volume 192 (2004), pp. 203-223

[10] F. Lárusson Mapping cylinders and the Oka principle, Indiana Univ. Math. J., Volume 54 (2005), pp. 1145-1159

[11] F. Lárusson What is an Oka manifold?, Notices Amer. Math. Soc., Volume 57 (2010) no. 1, pp. 50-52 http://www.ams.org/notices/201001/

[12] L. Vaserstein Reduction of a matrix depending on parameters to a diagonal form by addition operations, Proc. Amer. Math. Soc., Volume 103 (1988), pp. 741-746

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