Automorphism groups of P1-bundles over a non-uniruled base

Tatiana Bandman, Yu G. Zarhin

Research output: Contribution to journalArticlepeer-review


In this survey we discuss holomorphic P1-bundles p: X → Y over a non-uniruled complex compact Kähler manifold Y, paying a special attention to the case when Y is a complex torus. We consider the groups Aut(X) and Bim(X) of its biholomorphic and bimeromorphic automor-phisms, respectively, and discuss when these groups are bounded, Jordan, strongly Jordan, or very Jordan.

Original languageEnglish
Pages (from-to)1-64
Number of pages64
JournalRussian Mathematical Surveys
Issue number1
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 Russian Academy of Sciences, Steklov Mathematical Institute of RAS.


  • Jordan properties of groups
  • algebraic dimension 0
  • automorphism groups of compact complex manifolds
  • complex tori
  • conic bundles


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