Tits-type alternative for certain groups acting on algebraic surfaces

DOI10.1090/proc/16324OpenAlexW3212406929MaRDI QIDQ5889739

Mikhail Zaidenberg, Ivan V. Arzhantsev

Publication date: 27 April 2023

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.06659

zbMATH Keywords

group actionCremona groupTits alternativeaffine surfaceunipotent groupone-parameter subgroup

Mathematics Subject Classification ID

Birational automorphisms, Cremona group and generalizations (14E07) Group actions on varieties or schemes (quotients) (14L30) Group actions on affine varieties (14R20) Automorphisms of surfaces and higher-dimensional varieties (14J50) Groups as automorphisms of other structures (22F50)

Related Items

Automorphisms of hyperkähler manifolds and groups acting on CAT(0) spaces

Cites Work

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• On solvable subgroups of the Cremona group
• Topologies and structures of the Cremona groups
• The tame automorphism group of an affine quadric threefold acting on a square complex
• On the groups of birational transformations of surfaces
• Subgroups of elliptic elements of the Cremona group
• Automorphism group of a polynomial ring and algebraic group action on an affine space
• Abelian subgroups of \(Aut_ k(\)k[X,Y) and applications to actions on the affine plane]
• Rationally triangulable automorphisms
• On the absence of nontrivial separable forms of the affine plane
• Desingularization of two-dimensional schemes
• The amalgamated free product structure of \(\mathrm{GL}_2(k[X_1,\dots ,X_n )\) and the weak Jacobian theorem for two variables]
• Equivariant completion
• Flexible varieties and automorphism groups
• Infinite transitivity, finite generation, and Demazure roots
• Almost a building for the tame automorphism group
• On models of algebraic group actions
• Borel subgroups of the plane Cremona group
• Some finiteness results on triangular automorphisms
• On the nilpotent subgroups of the Cremona group
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Free subgroups in linear groups
• Smooth affine surfaces with non-unique ℂ*-actions
• Some Basic Theorems on Algebraic Groups
• Polarized Varieties, Fields of Moduli and Generalized Kummer Varieties of Polarized Abelian Varieties
• Lectures on Resolution of Singularities (AM-166)
• Some remarks on group actions on trees
• On the maximality of the triangular subgroup
• On automorphism groups of affine surfaces
• Bass' triangulability problem
• The Cremona Group and Its Subgroups
• Algebraic subgroups of the plane Cremona group over a perfect field
• Tits-type Alternative for Groups Acting on Toric Affine Varieties
• The Cremona group
• Sous-groupes algébriques de rang maximum du groupe de Cremona
• Über ganze birationale Transformationen der Ebene.
• On Algebraic Groups of Transformations
• The Tits alternative for \(\text{Aut}[\mathbb C^2\)]