Jordan property for Cremona groups

Abstract

Assuming Borisov--Alexeev--Borisov conjecture, we prove that there is a constant $J=J(n)$ such that for any rationally connected variety $X$ of dimension $n$ and any finite subgroup $G\subset Bir(X)$ there exists a normal abelian subgroup $A\subset G$ of index at most $J$. In particular, we obtain that the Cremona group $C{r}_3=Bir(P^3)$ enjoys the Jordan property.

13 pages, latex, Section 5 removed to appear as a separate preprint

References in corpus (2)

• Locally nilpotent derivations on affine surfaces with a $\C^*$-action
• Boundedness theorem for Fano log-threefolds

Cited by in corpus (1)

• Boosting an analogue of Jordan's theorem for finite groups