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Proceedings/Recueil Des Communications Année : 2023

Fibrations by affine lines on rational affine surfaces with irreducible boundaries

Résumé

We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that except for two exceptions, these surfaces $X \setminus B$ admit infinitely many families of $\mathbb{A}^1$-fibrations over the projective line with irreducible fibers and a unique singular fiber of arbitrarily large multiplicity. For $\mathbb{A}^1$-fibrations over the affine line, we give a new and essentially self-contained proof that the set of equivalence classes of such fibrations up to composition by automorphisms at the source and target is finite if and only if the self-intersection number of $B$ in $X$ is less than or equal to 6.
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Dates et versions

hal-03679747 , version 1 (27-05-2022)

Identifiants

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Adrien Dubouloz. Fibrations by affine lines on rational affine surfaces with irreducible boundaries. 409, Springer International Publishing, pp.225-248, 2023, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-031-17859-7_11⟩. ⟨hal-03679747⟩
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