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Journal Articles International Mathematics Research Notices Year : 2023

Connected algebraic groups acting on three-dimensional Mori fibrations

Abstract

We study the connected algebraic groups acting on Mori fibrations $X \to Y$ with $X$ a rational threefold and $\mathrm{dim}(Y) \geq 1$. More precisely, for these fibre spaces we consider the neutral component of their automorphism groups and study their equivariant birational geometry. This is done using, inter alia, minimal model program and Sarkisov program and allows us to determine the maximal connected algebraic subgroups of $\mathrm{Bir}(\mathbb{P}^3)$, recovering most of the classification results of Hiroshi Umemura in the complex case.
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Dates and versions

hal-02489771 , version 1 (27-10-2021)

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Jérémy Blanc, Andrea Fanelli, Ronan Terpereau. Connected algebraic groups acting on three-dimensional Mori fibrations. International Mathematics Research Notices, 2023, 2023 (2), pp.1572-1689. ⟨10.1093/imrn/rnab293⟩. ⟨hal-02489771⟩
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