Flexible varieties and automorphism groups
| Autor: | Shulim Kaliman, Hubert Flenner, Ivan Arzhantsev, Frank Kutzschebauch, Mikhail Zaidenberg |
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| Rok vydání: | 2010 |
| Předmět: |
Automorphism group
Transitive relation Pure mathematics 14L30 General Mathematics Algebraic variety Unipotent Automorphism 14R20 (Primary) 32M17 (Secondary) Mathematics - Algebraic Geometry Mathematics::Group Theory 510 Mathematics Tangent space FOS: Mathematics Affine transformation Locus (mathematics) Mathematics::Representation Theory 14R20 Algebraic Geometry (math.AG) Mathematics 32M17 |
| Zdroj: | Duke Math. J. 162, no. 4 (2013), 767-823 Arzhantsev, I.; Flenner, H.; Kaliman, S.; Kutzschebauch, F.; Zaidenberg, M. (2013). Flexible varieties and automorphism groups. Duke Mathematical Journal, 162(4), pp. 767-823. Duke University Press 10.1215/00127094-2080132 Duke Mathematical Journal |
| DOI: | 10.48550/arxiv.1011.5375 |
| 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: | OpenAIRE |
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