Finite quasisimple groups acting on rationally connected threefolds

Abstract

We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: ${\mathfrak{A}}_5$, ${\mathrm{PSL}}_2({\mathbf{F}}_7)$, ${\mathfrak{A}}_6$, ${\mathrm{SL}}_2({\mathbf{F}}_8)$, ${\mathfrak{A}}_7$, ${\mathrm{PSp}}_4({\mathbf{F}}_3)$, ${\mathrm{SL}}_2({\mathbf{F}}_7)$, $2.{\mathfrak{A}}_5$, $2.{\mathfrak{A}}_6$, $3.{\mathfrak{A}}_6$ 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.

41 pages