An affine variety of dimension ≥ 2 is called flexible if its special automorphism group SAut() acts transitively on the smooth locus . Recall that SAut() is the subgroup of the automorphism group Aut() generated by all one-parameter unipotent subgroups . Given a normal, flexible, affine variety and a closed subvariety in of codimension at least 2, we show that the pointwise stabilizer subgroup of in the group SAut() acts infinitely transitively on the complement , that is, -transitively for any . More generally we show such a result for any quasi-affine variety and codimension ≥ 2 subset of .
In the particular case of , n ≥ 2, this yields a Theorem of Gromov and Winkelmann , .
Cite this article
Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg, A Gromov–Winkelmann type theorem for flexible varieties. J. Eur. Math. Soc. 18 (2016), no. 11, pp. 2483–2510DOI 10.4171/JEMS/646