Locally nilpotent derivations on affine surfaces with a $\C^*$-action

Hubert Flenner (1) , Mikhail Zaidenberg (2)

1 Fakultät für Mathematik - Fakultät für Mathematik
2 IF - Institut Fourier

We give a classification of normal affine surfaces admitting an algebraic group action with an open orbit. In particular an explicit algebraic description of the affine coordinate rings and the defining equations of such varieties is given. By our methods we recover many known results, e.g. the classification of normal affine surfaces with a `big' open orbit of Gizatullin and Popov or some of the classification results of Danilov-Gizatullin, Bertin and others.

Mots clés: affine surface; cyclic quotient singularity; graded algebra; $\C_+$-action; $\C^*$-action

Domaines: Géométrie algébrique [math.AG]

Hubert Flenner, Mikhail Zaidenberg. Locally nilpotent derivations on affine surfaces with a $\C^*$-action. Osaka Journal of Mathematics, 2005, 42 (4), pp.931-974. ⟨hal-00001286⟩