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arXiv · 1211.3563

Jordan property for Cremona groups

Yuri Prokhorov·Constantin Shramov
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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 $Cr_3=Bir(P^3)$ enjoys the Jordan property.

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Yuri Prokhorov, Constantin Shramov. 2014-06-01. Jordan property for Cremona groups. https://arxiv.org/abs/1211.3563

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