A projective variety with discrete, non-finitely generated automorphism group

Lesieutre, John

doi:10.1007/s00222-017-0766-9

Cited by 28 publications

(37 citation statements)

References 18 publications

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“…For all n ≥ 2, there exists a smooth projective simply connected ndimensional variety X over C such that Aut 0 X /C is trivial and Aut C (X ) is a non-finitely generated (infinite, non-torsion) group; see [37]. Note that the arguments and ideas in loc.…”

Section: Remark 512mentioning

confidence: 99%

Arithmetic hyperbolicity: automorphisms and persistence

Javanpeykar

2021

Math. Ann.

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We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang’s conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many rational points has only finitely many automorphisms. Moreover, we investigate to what extent finiteness of S-integral points on a variety over a number field persists over finitely generated fields. To this end, we introduce the class of mildly bounded varieties and prove a general criterion for proving this persistence.

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Section: Remark 512mentioning

confidence: 99%

Arithmetic hyperbolicity: automorphisms and persistence

Javanpeykar

2021

Math. Ann.

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“…The long-standing question whether this group is finitely generated has been recently answered in the negative by Lesieutre. He constructed an example of a smooth projective variety of dimension 6 having a discrete, non-finitely generated automorphism group (see [Les18]). His construction has been extended in all dimensions at least 2 by Dinh and Oguiso (see [DO19]).…”

Section: ])mentioning

confidence: 99%

Subgroups of elliptic elements of the Cremona group

Urech

2021

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the structure of torsion subgroups. As an application, we prove the Tits alternative for arbitrary subgroups of the Cremona group, generalizing a result of Cantat. We also describe solvable subgroups of the Cremona group and their derived length, refining results from Déserti.

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“…Recently, Lesieutre proved that if k is a field of characteristic 0, or a field which is not algebraic over its prime field, then there is a smooth, 6-dimensional projective variety X over k such that Aut(X) 0 is trivial and Aut(X) * is not finitely generated (see [34] and [20] for another example). This shows that it is somewhat artificial to assume that Γ is finitely generated.…”

Section: Remark 23mentioning

confidence: 99%