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Pré-Publication, Document De Travail Année : 2018

INFINITE TRANSITIVITY, FINITE GENERATION, AND DEMAZURE ROOTS

I Arzhantsev
  • Fonction : Auteur
K Kuyumzhiyan
  • Fonction : Auteur
M Zaidenberg

Résumé

An affine algebraic variety X of dimension ≥ 2 is called flexible if the subgroup SAut(X) ⊂ Aut(X) generated by the one-parameter unipotent subgroups acts m-transitively on reg (X) for any m ≥ 1. In a preceding paper ([4]) we proved that any nondegenerate toric affine variety X is flexible. Here we show that if such a toric variety X is smooth in codimension 2 then one can find a subgroup of SAut(X) generated by a finite number of one-parameter unipotent subgroups which has the same transitivity property. In fact, four such subgroups are enough for X = A n if n ≥ 3, and just three if n = 2.
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Dates et versions

hal-01745146 , version 1 (27-03-2018)
hal-01745146 , version 2 (27-08-2018)

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I Arzhantsev, K Kuyumzhiyan, M Zaidenberg. INFINITE TRANSITIVITY, FINITE GENERATION, AND DEMAZURE ROOTS. 2018. ⟨hal-01745146v2⟩
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