### 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 (US) |
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Pages (from-to) | 721-739 |

Number of pages | 19 |

Journal | Transformation Groups |

Volume | 24 |

Issue number | 3 |

DOIs | |

State | Published - Sep 15 2019 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Transformation Groups*,

*24*(3), 721-739. https://doi.org/10.1007/s00031-018-9489-2

}

*Transformation Groups*, vol. 24, no. 3, pp. 721-739. https://doi.org/10.1007/s00031-018-9489-2

**JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES.** / Bandman, Tatiana; Zarhin, Yuri G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES

AU - Bandman, Tatiana

AU - Zarhin, Yuri G.

PY - 2019/9/15

Y1 - 2019/9/15

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.

UR - http://www.scopus.com/inward/record.url?scp=85051570286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051570286&partnerID=8YFLogxK

U2 - 10.1007/s00031-018-9489-2

DO - 10.1007/s00031-018-9489-2

M3 - Article

AN - SCOPUS:85051570286

VL - 24

SP - 721

EP - 739

JO - Transformation Groups

JF - Transformation Groups

SN - 1083-4362

IS - 3

ER -