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Jordan property for Cremona groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 138, Number 2, April 2016
- pp. 403-418
- 10.1353/ajm.2016.0017
- Article
- Additional Information
Assuming the 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 $G\subset{\rm Bir}(X)$ there exists
a normal abelian subgroup $A\subset G$ of index at most $J$. In
particular, we obtain that the Cremona group ${\rm Cr}_3={\rm Bir}({\Bbb
P}^3)$ enjoys the Jordan property.