Geodesic
A Gromov–Winkelmann type theorem for flexible varieties
Journal of the European Mathematical Society, Tome 18 (2016) no. 11, pp. 2483-2510

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An affine variety X of dimension ≥ 2 is called flexible if its special automorphism group SAut(X) acts transitively on the smooth locus Xreg​ [1]. Recall that SAut(X) is the subgroup of the automorphism group Aut(X) generated by all one-parameter unipotent subgroups [1]. 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 show such a result for any quasi-affine variety X and codimension ≥ 2 subset Y of X.
DOI : 10.4171/jems/646
Classification : 14-XX, 32-XX
Keywords: Affine varieties, group actions, one-parameter subgroups, transitivity 
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     title = {A {Gromov{\textendash}Winkelmann} type theorem for flexible varieties},
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     pages = {2483--2510},
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Hubert Flenner; Shulim Kaliman; Mikhail Zaidenberg. A Gromov–Winkelmann type theorem for flexible varieties. Journal of the European Mathematical Society, Tome 18 (2016) no. 11, pp. 2483-2510. doi: 10.4171/jems/646

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