p-subgroups in the space Cremona group

Abstract

We prove that if $X$ is a rationally connected threefold and $G$ is a $p$-subgroup in the group of birational selfmaps of $X$, then $G$ is an abelian group generated by at most $3$ elements provided that $p\ge 17$. We also prove a similar result for $p\ge 11$ under an assumption that $G$ acts on a (Gorenstein) $G$-Fano threefold, and show that the same holds for $p\ge 5$ under an assumption that $G$ acts on a $G$-Mori fiber space.

27 pages, LaTeX, few corrections, numeration of statements is shifted

References in corpus (1)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds

Cited by in corpus (2)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Finite $p$-groups of birational automorphisms and characterizations of rational varieties