Complete algebraic vector fields on Danielewski surfaces

Leuenberger, Matthias (2016). Complete algebraic vector fields on Danielewski surfaces. Annales de l'Institut Fourier, 66(2), pp. 433-454. Association des Annales de l'Institut Fourier 10.5802/aif.3015

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We give the classification of all complete algebraic vector fields on Danielewski surfaces (smooth surfaces given by xy=p(z)). We use the fact that for each such vector field there exists a certain fibration that is preserved under its flow. In order to get the explicit list of vector fields a classification of regular function with general fiber ℂ or ℂ * is required. In this text we present results about such fibrations on Gizatullin surfaces and we give a precise description of these fibrations for Danielewski surfaces.

Item Type:

Journal Article (Original Article)

Division/Institute:

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

UniBE Contributor:

Leuenberger, Matthias

Subjects:

500 Science > 510 Mathematics

ISSN:

1777-5310

Publisher:

Association des Annales de l'Institut Fourier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

12 Jul 2017 10:49

Last Modified:

12 Jul 2017 10:49

Publisher DOI:

10.5802/aif.3015

ArXiv ID:

1411.6493v2

BORIS DOI:

10.7892/boris.98618

URI:

https://boris.unibe.ch/id/eprint/98618

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