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, Werner Frank, 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: |
05 Dec 2022 15:04 |
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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