Automorphisms of $\mathbb{A}^{1}$-fibered affine surfaces

DOI10.1090/S0002-9947-2011-05266-9zbMath1239.14053arXiv0906.3623OpenAlexW1600370598MaRDI QIDQ3103242

Adrien Dubouloz, Jérémy Blanc

Publication date: 7 December 2011

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

Full work available at URL: https://arxiv.org/abs/0906.3623

zbMATH Keywords

automorphismbirational morphismaffine surface\(\mathbb{A}^1\)-fibrationstandard completionGizatullin surface

Mathematics Subject Classification ID

Classification of affine varieties (14R05) Rational and birational maps (14E05) Group actions on affine varieties (14R20) Affine fibrations (14R25)

Related Items

Smooth rational affine varieties with infinitely many real forms ⋮ Pointed Hopf actions on quantum generalized Weyl algebras ⋮ Fake real planes: exotic affine algebraic models of \(\mathbb {R}^{2}\) ⋮ Complete algebraic vector fields on Danielewski surfaces ⋮ Automorphisms of open surfaces with irreducible boundary ⋮ Fibrations by affine lines on rational affine surfaces with irreducible boundaries ⋮ Complete intersection surfaces with trivial Makar-Limanov invariant ⋮ Real forms of some Gizatullin surfaces and Koras-Russell threefolds ⋮ Embeddings of affine spaces into quadrics ⋮ Affine lines in the complement of a smooth plane conic ⋮ Non-rationality of some fibrations associated to Klein surfaces ⋮ Automorphisms and isomorphisms of quantum generalized Weyl algebras. ⋮ Super-rigid affine Fano varieties ⋮ Real frontiers of fake planes

Cites Work

• On the structure of the automorphism group of certain affine surfaces
• On groups of automorphisms of a class of surfaces
• Affine surfaces with \(AK(S)=\mathbb C\).
• A geometric proof of a theorem of Jung
• On locally nilpotent derivations of \(k[X_{1},X_{2},Y/ (\varphi(Y)-X_{1} X_{2})\). -- Appendix: Rationality of certain affine plane curves.]
• Completions of normal affine surfaces with a trivial Makar-Limanov invariant
• Embeddings of Danielewski surfaces in affine spaces
• Open Algebraic Surfaces
• A new geometric proof of Jung’s theorem on factorisation of automorphisms of ℂ²
• Über ganze birationale Transformationen der Ebene.
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