May 28, 2024Open Access

Automorphisms of unstable P¹-bundles

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Abstract

Let P X be a P¹-bundle over a variety X. The aim of this note is to understand all connected, algebraic groups Aut^ (P) G Bir (X P¹). We get a quite complete answer if Aut^ (X) is a maximal, connected, algebraic subgroup of Bir (X), and P is sufficiently unstable. This gives examples of connected, algebraic subgroups of Bir (P⁴) that are not contained in any maximal one.

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Janós Kollár (Tue,) studied this question.

synapsesocial.com/papers/68e68219b6db64358760aa53 https://doi.org/https://doi.org/10.48550/arxiv.2405.18201

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