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Article Dans Une Revue Osaka Journal of Mathematics Année : 2003

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

Hubert Flenner
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Mikhail Zaidenberg

Résumé

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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Dates et versions

hal-00001681 , version 1 (11-06-2004)
hal-00001681 , version 2 (14-06-2004)

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Citer

Hubert Flenner, Mikhail Zaidenberg. Normal affine surfaces with $\bf C^*$-actions. Osaka Journal of Mathematics, 2003, 40 (4), pp.981-1009. ⟨hal-00001681v2⟩

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