Flexible varieties and automorphism groups
| Autor: | Arzhantsev, I., Flenner, H., Kaliman, S., Kutzschebauch, F., Zaidenberg, M. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Duke Math. J. 162, no. 4 (2013), 767-823 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1215/00127094-2080132 |
| Popis: | Given an affine algebraic variety X of dimension at least 2, we let SAut (X) denote the special automorphism group of X i.e., the subgroup of the full automorphism group Aut (X) generated by all one-parameter unipotent subgroups. We show that if SAut (X) is transitive on the smooth locus of X then it is infinitely transitive on this locus. In turn, the transitivity is equivalent to the flexibility of X. The latter means that for every smooth point x of X the tangent space at x is spanned by the velocity vectors of one-parameter unipotent subgroups of Aut (X). We provide also different variations and applications. Comment: Final version; to appear in Duke Math. J |
| Databáze: | arXiv |
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