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Flexible varieties and automorphism groups

Monday, 6 June, 2011 - 12:30
Prénom de l'orateur : 
Shulim
Nom de l'orateur : 
KALIMAN
Résumé : 

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
X_reg then it is infinitely transitive on X_reg. In
turn, the transitivity is equivalent to the flexibility of X.
The latter means that for every smooth point x in X_reg the
tangent space of X at x is spanned by the velocity vectors at x of
one-parameter unipotent subgroups of Aut (X). We provide also
different variations and applications.

Institution de l'orateur : 
Université de Miami
Thème de recherche : 
Algèbre et géométries
Salle : 
04
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