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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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