A Gromov-Winkelmann type theorem for flexible varieties

被引：20

作者：

Flenner, Hubert ^{[1
]}

Kaliman, Shulim ^{[2
]}

Zaidenberg, Mikhail ^{[3
]}

机构：

[1] Ruhr Univ Bochum, Fak Math, Geb NA 2-72,Univ Str 150, D-44780 Bochum, Germany

[2] Univ Miami, Dept Math, Coral Gables, FL 33124 USA

[3] Univ Grenoble 1, Inst Fournier, CNRS UJF, UMR 5582, BP 74, F-38402 St Martin Dheres, France

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2016年 / 18卷 / 11期

关键词：

Affine varieties; group actions; one-parameter subgroups; transitivity;

D O I：

10.4171/JEMS/646

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An affine variety X of dimension >= 2 is called flexible if its special automorphism group SAut (X) acts transitively on the smooth locus X-reg. Recall that SAut. (X) is the subgroup of the automorphism group Aut. (X) generated by all one-parameter unipotent subgroups [2]. Given a normal, flexible, affine variety X and a closed subvariety Y in X of codimension at least 2, we show that the pointwise stabilizer subgroup of Y in the group SAut. (X) acts infinitely transitively on the complement X \ Y, that is, m-transitively for any m >= 1. More generally we prove such a result for any quasi-affine variety X and codimension >= 2 subset Y of X. In the particular case of X = A(n), n >= 2, this yields a theorem of Gromov and Winkelmann [8], [18].

引用

页码：2483 / 2510

页数：28

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