Automorphisms of $\mathbb{P}^1$-bundles over rational surfaces

Jérémy Blanc (1) , Andrea Fanelli (2) , Ronan Terpereau (3)

1 Unibas - Université de Bâle = University of Basel = Basel Universität
2 IMB - Institut de Mathématiques de Bordeaux
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]

In this paper we provide the complete classification of $\mathbb{P}^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of characteristic zero.

Domaines: Géométrie algébrique [math.AG]

Jérémy Blanc, Andrea Fanelli, Ronan Terpereau. Automorphisms of $\mathbb{P}^1$-bundles over rational surfaces. 2017. ⟨hal-01620406v1⟩