Automorphisms of 𝔸¹-fibered affine surfaces

Blanc, Jérémy; Dubouloz, Adrien

doi:10.1090/S0002-9947-2011-05266-9

Automorphisms of $\mathbb {A}^{1}$-fibered affine surfaces
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by Jérémy Blanc and Adrien Dubouloz PDF

Trans. Amer. Math. Soc. 363 (2011), 5887-5924 Request permission

Abstract:

We develop techniques of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface $S$ of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of $S$ is generated by automorphisms preserving these fibrations.

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