Oka maps

Franc Forstnerič

doi:10.1016/j.crma.2009.12.004

Complex Analysis

Oka maps

Presented by: Mikhaël Gromov

Franc Forstnerič ¹

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.

Abstract
Résumé

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.

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.

Received: 2009-11-11
Accepted: 2009-12-07
Published online: 2009-12-30

DOI: 10.1016/j.crma.2009.12.004

Author's affiliations:

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/

References
Cited by

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

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[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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