Locally nilpotent derivations on affine surfaces with a \(\mathbb C^*\)-action. (English) Zbl 1140.14323

Flenner, Hubert; Zaidenberg, Mikhail

Osaka J. Math. 42, No. 4, 931-974 (2005).

Summary: 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 M. H. Gizatullin [Math. USSR, Izv. 5(1971), 1057–1081 (1972; Zbl 0249.14010)] and V. L. Popov [Izv. Akad. Nauk SSSR, Ser. Mat. 37, 1038–1055 (1973; Zbl 0251.14018)] or some of the classification results of V. I. Danilov-M.H. Gizatullin [Math. USSR, Izv. 9(1975), 493–534 (1976; Zbl 0331.14007)], J. Bertin [J. Reine Angew. Math. 341, 32–53 (1983; Zbl 0501.14028)] and others.

MSC:

14R20	Group actions on affine varieties
14R05	Classification of affine varieties

Citations:

Zbl 0249.14010; Zbl 0251.14018; Zbl 0331.14007; Zbl 0501.14028