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arXiv · 2310.19597

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

Pascal Fong
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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.

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Pascal Fong. 2023-10-30. Automorphism groups of $\mathbb{P}^1$-bundles over geometrically ruled surfaces. https://arxiv.org/abs/2310.19597

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