Abstract:
The paper reviews the results of recent years on the multiple transitivity
of actions of the automorphism groups of affine algebraic varieties.
The property of infinite transitivity for the action of the group of
special automorphisms is considered and the equivalent flexibility property of the variety.
These properties have important algebraic and geometric consequences,
and at the same time they are fulfilled for wide classes of manifolds.
The cases when infinite transitivity
occurs for automorphism groups generated by a finite number
of one-parameter subgroups are studied separately.
In the appendices to the paper, the results on infinitely
transitive actions in complex analysis and in combinatorial group theory are considered.
Citation:
I. Arzhantsev, “Automorphisms of algebraic varieties and infinite transitivity”, Algebra i Analiz, 34:2 (2022), 1–55; St. Petersburg Math. J., 34:2 (2023), 143–178
\Bibitem{Arz22}
\by I.~Arzhantsev
\paper Automorphisms of algebraic varieties and infinite transitivity
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 2
\pages 1--55
\mathnet{http://mi.mathnet.ru/aa1800}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4382685}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 2
\pages 143--178
\crossref{https://doi.org/10.1090/spmj/1749}
Linking options:
https://www.mathnet.ru/eng/aa1800
https://www.mathnet.ru/eng/aa/v34/i2/p1
This publication is cited in the following 3 articles:
Alexander Perepechko, “Generic Flexibility of Affine Cones over Del Pezzo Surfaces in Sagemath”, Taiwanese J. Math., -1:-1 (2025)
Shulim Kaliman, Mikhail Zaidenberg, “Gromov ellipticity and subellipticity”, Forum Mathematicum, 36:2 (2024), 373
Nguyen Thi Anh Hang, Hoang Le Truong, “The Affine Cones Over Fano–Mukai Fourfolds of Genus 7 Are Flexible”, International Mathematics Research Notices, 2024:10 (2024), 8417
Citation in format AMSBIB
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