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Journal Article

#### Jordan properties of automorphism groups of certain open algebraic varieties

##### External Resource

https://doi.org/10.1007/s00031-018-9489-2

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##### Fulltext (public)

arXiv:1705.07523.pdf

(Preprint), 258KB

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##### Citation

Bandman, T., & Zarhin, Y. G. (2019). Jordan properties of automorphism groups of
certain open algebraic varieties.* Transformation Groups,* *24*(3),
721-739. doi:10.1007/s00031-018-9489-2.

Cite as: https://hdl.handle.net/21.11116/0000-0004-59ED-E

##### 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 $\mathcal{B}$ of ${G}$ contains a commutative subgroup $\mathcal{A}$

such that $\mathcal{A}$ is normal in $\mathcal{B}$ and the index

$[\mathcal{B}:\mathcal{A}] \le J$ .

subgroup $\mathcal{B}$ of ${G}$ contains a commutative subgroup $\mathcal{A}$

such that $\mathcal{A}$ is normal in $\mathcal{B}$ and the index

$[\mathcal{B}:\mathcal{A}] \le J$ .