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.
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Franc Forstnerič 1
@article{CRMATH_2010__348_3-4_145_0, author = {Franc Forstneri\v{c}}, title = {Oka maps}, journal = {Comptes Rendus. Math\'ematique}, pages = {145--148}, publisher = {Elsevier}, volume = {348}, number = {3-4}, year = {2010}, doi = {10.1016/j.crma.2009.12.004}, language = {en}, }
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/
[1] The Oka principle for sections of subelliptic submersions, Math. Z., Volume 241 (2002), pp. 527-551
[2] Oka manifolds, C. R. Acad. Sci. Paris Ser. I, Volume 347 (2009), pp. 1017-1020
[3] The Oka principle for sections of stratified fiber bundles, Pure Appl. Math. Q., Volume 6 (2010) no. 3, pp. 843-874
[4] Invariance of the parametric Oka property (P. Ebenfelt; N. Hungerbuehler; J.J. Kohn; N. Mok; E.J. Straube, eds.), Complex Analysis, Trends Math., Birkhäuser, 2010
[5] Oka's principle for holomorphic submersions with sprays, Math. Ann., Volume 322 (2002), pp. 633-666
[6] Fibrations and Stein neighborhoods (Proc. Amer. Math. Soc., in press) | arXiv
[7] Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc., Volume 2 (1989), pp. 851-897
[8] A solution of Gromov's Vaserstein problem, C. R. Acad. Sci. Paris Ser. I, Volume 346 (2008), pp. 1239-1243
[9] Model structures and the Oka principle, J. Pure Appl. Algebra, Volume 192 (2004), pp. 203-223
[10] Mapping cylinders and the Oka principle, Indiana Univ. Math. J., Volume 54 (2005), pp. 1145-1159
[11] What is an Oka manifold?, Notices Amer. Math. Soc., Volume 57 (2010) no. 1, pp. 50-52 http://www.ams.org/notices/201001/
[12] 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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