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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Automorphisms of algebraic varieties and infinite transitivity
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by I. Arzhantsev
Translated by: the author
St. Petersburg Math. J. 34 (2023), 143-178
Published electronically: March 22, 2023


This is a survey of recent results on multiple transitivity for automorphism groups of affine algebraic varieties. The property of infinite transitivity of the special automorphism group is treated, which is equivalent to the flexibility of the corresponding affine variety. These properties have important algebraic and geometric consequences. At the same time they are fulfilled for wide classes of varieties. Also, the situations are studied where infinite transitivity occurs for automorphism groups generated by finitely many one-parameter subgroups. In the appendices to the paper, the results on infinitely transitive actions in complex analysis and in combinatorial group theory are discussed.
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Bibliographic Information
  • I. Arzhantsev
  • Affiliation: Faculty of Computer Science, HSE University, Pokrovsky Boulevard 11, Moscow 109028, Russia
  • MR Author ID: 359575
  • Email:
  • Received by editor(s): August 29, 2021
  • Published electronically: March 22, 2023
  • Additional Notes: Supported by Russian Foundation for Basic Research, grant 20-11-50106
  • © Copyright 2023 American Mathematical Society
  • Journal: St. Petersburg Math. J. 34 (2023), 143-178
  • MSC (2020): Primary 14L30, 14R10; Secondary 13E10, 14M25, 20M32
  • DOI: