JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES

Tatiana Bandman; Yuri G. Zarhin

doi:10.1007/s00031-018-9489-2

JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES

Tatiana Bandman, Yuri G. Zarhin

Department of Mathematics

Pennsylvania State University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let W be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that W is birational to a product of a smooth projective variety A and the projective line. We prove that if A contains no rational curves then the automorphism group G := Aut (W) of W is Jordan. That means that there is a positive integer J = J (W) such that every finite subgroup ℬ of G contains a commutative subgroup A such that A is normal in ℬ and the index [ℬ : A] ≤ J.

Original language	English
Pages (from-to)	721-739
Number of pages	19
Journal	Transformation Groups
Volume	24
Issue number	3
DOIs	https://doi.org/10.1007/s00031-018-9489-2
State	Published - 15 Sep 2019

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© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

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abstract = "Let W be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that W is birational to a product of a smooth projective variety A and the projective line. We prove that if A contains no rational curves then the automorphism group G := Aut (W) of W is Jordan. That means that there is a positive integer J = J (W) such that every finite subgroup ℬ of G contains a commutative subgroup A such that A is normal in ℬ and the index [ℬ : A] ≤ J.",

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N2 - Let W be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that W is birational to a product of a smooth projective variety A and the projective line. We prove that if A contains no rational curves then the automorphism group G := Aut (W) of W is Jordan. That means that there is a positive integer J = J (W) such that every finite subgroup ℬ of G contains a commutative subgroup A such that A is normal in ℬ and the index [ℬ : A] ≤ J.

AB - Let W be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that W is birational to a product of a smooth projective variety A and the projective line. We prove that if A contains no rational curves then the automorphism group G := Aut (W) of W is Jordan. That means that there is a positive integer J = J (W) such that every finite subgroup ℬ of G contains a commutative subgroup A such that A is normal in ℬ and the index [ℬ : A] ≤ J.

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JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES

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