Flexible affine cones and flexible coverings

Michałek, Mateusz; Perepechko, Alexander; Süß, Hendrik

doi:10.1007/s00209-018-2069-2

Cited by 14 publications

(13 citation statements)

References 41 publications

(55 reference statements)

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“…Besides the toric affine varieties with no torus factor there are several other interesting classes of flexible affine varieties, see, e.g., [3,4,5,6,17,40,41,42,44,45,47].…”

mentioning

confidence: 99%

Infinite transitivity, finite generation, and Demazure roots

Arzhantsev

Kuyumzhiyan

Zaidenberg

2019

Advances in Mathematics

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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 [4] we proved that any nondegenerate toric affine variety X is flexible. In the present paper we show that one can find a subgroup of SAut(X) generated by a finite number of one-parameter unipotent subgroups which has the same transitivity property, provided the toric variety X is smooth in codimension two. For X = A n with n ≥ 2, three such subgroups suffice. G a -subgroup, for short. One can consider the subgroup SAut(X) ⊂ Aut(X) generated by all the one-parameter unipotent subgroups. It is known ([4, Thm. 2.1]) that for a toric affine variety X with no torus factor (that is, a nondegenerate toric variety) the group SAut(X) acts infinitely transitively on the smooth locus reg(X), that is, m-transitively for any m ≥ 1. Varieties X with this property are called flexible ([3, 4]). Actually, the simple transitivity of

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“…Besides the toric affine varieties with no torus factor there are several other interesting classes of flexible affine varieties, see, e.g., [3,4,5,6,17,40,41,42,44,45,47].…”

mentioning

confidence: 99%

Infinite transitivity, finite generation, and Demazure roots

Arzhantsev

Kuyumzhiyan

Zaidenberg

2019

Advances in Mathematics

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“…The second useful criterion is given by the following Theorem 4.12 ( [149]). The affine cone y V is flexible if the variety V is uniformly cylindrical and admits a covering…”

Section: Affine Cones Over Cylindrical Fano Varieties Often Provide Examples Of Flexible Affine Varietiesmentioning

confidence: 99%

Cylinders in Fano varieties

Cheltsov

Park

Prokhorov

et al. 2021

EMS Surv. Math. Sci.

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“…In Section 2 we provide a criterion of flexibility in codimension one for affine cones, which generalizes similar flexibility criteria in our previous articles [8] and [10]. In Section 3 we recall generalities on cubic surfaces.…”

Section: Introductionmentioning

confidence: 97%