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

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

2002-10-10

arxiv.org/abs/math/0210153v1

Mathematics

Algebraic Geometry

Uses P.Taylor's diagrams.tex

Scientific paper

A classification of normal affine surfaces admitting a $\bf C^*$-action was given in the work of Bia{\l}ynicki-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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