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Finite quasisimple groups acting on rationally connected threefolds
Published online by Cambridge University Press: 06 December 2022
Abstract
We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: ${\mathfrak{A}}_5$ , ${\text{PSL}}_2(\textbf{F}_7)$ , ${\mathfrak{A}}_6$ , ${\text{SL}}_2(\textbf{F}_8)$ , ${\mathfrak{A}}_7$ , ${\text{PSp}}_4(\textbf{F}_3)$ , ${\text{SL}}_2(\textbf{F}_{7})$ , $2.{\mathfrak{A}}_5$ , $2.{\mathfrak{A}}_6$ , $3.{\mathfrak{A}}_6$ or $6.{\mathfrak{A}}_6$ . All of these groups with a possible exception of $2.{\mathfrak{A}}_6$ and $6.{\mathfrak{A}}_6$ indeed act on some rationally connected threefolds.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 3 , May 2023 , pp. 531 - 568
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
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