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 \( \mathcal{A} \) such that \( \mathcal{A} \) is normal in ℬ and the index \( \left[\mathrm{\mathcal{B}}:\mathcal{A}\right]\le J \).
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During the preparation of this paper the second named author was partially supported by a grant from the Simons Foundation (#246625 to Yuri Zarkhin). Part of this work was done in May–June 2016 during his stay at the Max-Planck-Institut für Mathematik, whose hospitality and support are gratefully acknowledged.
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BANDMAN, T., ZARHIN, Y.G. JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES. Transformation Groups 24, 721–739 (2019). https://doi.org/10.1007/s00031-018-9489-2
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DOI: https://doi.org/10.1007/s00031-018-9489-2