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Normal affine surfaces with $\bf C^*$-actions

Hubert Flenner·Mikhail Zaidenberg
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Abstract

A classification of normal affine surfaces admitting a $\bf C^*$-action was given in the work of Białynicki-Birula, Fieseler and L. Kaup, Orlik and Wagreich, Rynes and others. We provide a simple alternative description of such surfaces in terms of their graded rings as well as by defining equations. This is based on a generalization of the Dolgachev-Pinkham-Demazure construction in the case of a hyperbolic grading. As an apllication we determine the structure of singularities, of the orbits and the divisor class groups for such surfaces.

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Hubert Flenner, Mikhail Zaidenberg. 2002-10-10. Normal affine surfaces with $\bf C^*$-actions. https://arxiv.org/abs/math/0210153

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