An Oka Principle for a Parametric Infinite Transitivity Property

Kutzschebauch, Frank; Ramos Peon, Alexandre (2017). An Oka Principle for a Parametric Infinite Transitivity Property. Journal of geometric analysis, 27(3), pp. 2018-2043. Springer 10.1007/s12220-016-9749-0

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It is an elementary fact that the action by holomorphic automorphisms on Cn is infinitely transitive, i.e., m-transitive for any m∈N. The same holds on any Stein manifold with the holomorphic density property X. We study a parametrized case: we consider m points on X parametrized by a Stein manifold W, and seek a family of automorphisms of X, parametrized by W, putting them into a standard form which does not depend on the parameter. This general transitivity is shown to enjoy an Oka principle, to the effect that the obstruction to a holomorphic solution is of a purely topological nature. In the presence of a volume form and of a corresponding density property, similar results for volume-preserving automorphisms are obtained.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Kutzschebauch, Frank and Ramos Peon, Alexandre

Subjects:

500 Science > 510 Mathematics

ISSN:

1050-6926

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

29 Jun 2017 09:13

Last Modified:

18 Nov 2017 02:30

Publisher DOI:

10.1007/s12220-016-9749-0

BORIS DOI:

10.7892/boris.98623

URI:

https://boris.unibe.ch/id/eprint/98623

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