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arXiv · 1411.6493

Complete Algebraic Vector Fields on Danielewski Surfaces

Matthias Leuenberger
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Abstract

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 $\mathbb{C}$ or $\mathbb{C}^*$ 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.

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Matthias Leuenberger. 2014-11-24. Complete Algebraic Vector Fields on Danielewski Surfaces. https://arxiv.org/abs/1411.6493

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