Automorphism groups of $\mathbb{P}^1$-bundles over geometrically ruled surfaces

Pascal Fong

Automorphism groups of $\mathbb{P}^1$-bundles over geometrically ruled surfaces

Algebraic Geometry 2026-05-19 v5

Authors: Pascal Fong

Abstract

We classify the pairs $(X,\pi)$ , where $\pi\colon X\to S$ is a $\mathbb{P}^1$ -bundle over a non-rational geometrically ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the group $\mathrm{Bir}(X/S)$ . The results hold over any algebraically closed field of characteristic zero.

Keywords

automorphism groups p1-bundles geometrically ruled surfaces birational geometry algebraically closed field

Cite

@article{arxiv.2310.19597,
  title  = {Automorphism groups of $\mathbb{P}^1$-bundles over geometrically ruled surfaces},
  author = {Pascal Fong},
  journal= {arXiv preprint arXiv:2310.19597},
  year   = {2026}
}

Comments

To appear in Journal of the London Mathematical Society

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