Jordan properties of automorphism groups of certain open algebraic varieties

Bandman, Tatiana; Zarhin, Yuri G.

doi:10.1007/s00031-018-9489-2

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Jordan properties of automorphism groups of certain open algebraic varieties

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Zarhin, Yuri G.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00031-018-9489-2
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arXiv:1705.07523.pdf
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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
$[\mathcal{B}:\mathcal{A}] \le J$ .