Jordan constant for Cremona group of rank 3

TL;DR

This paper provides explicit bounds for the Jordan constants of groups of birational automorphisms of rationally connected threefolds, focusing on Cremona groups of ranks 2 and 3, over fields of zero characteristic.

Contribution

It offers the first explicit bounds for Jordan constants of Cremona groups of rank 3, extending previous results to three-dimensional cases.

Findings

Explicit bounds for Jordan constants of Cremona groups of rank 2 and 3.

Application to groups of birational automorphisms of rationally connected threefolds.

Results valid over fields of zero characteristic.

Abstract

We give explicit bounds for Jordan constants of groups of birational automorphisms of rationally connected threefolds over fields of zero characteristic, in particular, for Cremona groups of ranks 2 and 3.