Jordan property for Cremona groups

By Yuri Prokhorov, Constantin Shramov. 2012

96 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/789408b5fe09a0050861756b5a5fc2d7e976e6ed

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. V. Popov
2. Constantin Shramov
3. Yuri Prokhorov
4. Alexander Kuznetsov

In Geometry and Topology

1. Yuri Prokhorov
2. Constantin Shramov
3. V. Popov
4. Alexander Kuznetsov
5. K. Hori
6. Emanuele Macrì
7. P. Stellari
8. Alexander Perry

In Mathematical Physics

1. Constantin Shramov
2. Yuri Prokhorov
3. V. Popov
4. Alexander Kuznetsov
5. K. Hori
6. Emanuele Macrì
7. P. Stellari
8. Alexander Perry

Citations in the corpus

• Jordan groups and automorphism groups of algebraic varieties (2013, background): “Below are formulated the results obtained in [PS20131], [PS20132].”
• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds (2016, background): “group. Note that besides just proving niteness, this approach allows to give explicit upper bounds on some parameters of automorphism groups, which may be useful for further applications (cf. [PS14], [PS16]). Finally, in x4.4 we prove niteness of the automorphism groups in the remaining (easy) cases”