The Jordan property of Cremona groups and essential dimension

TL;DR

This paper leverages recent advances in birational geometry to establish new lower bounds on the essential dimension of certain finite groups, enhancing understanding of their algebraic complexity.

Contribution

It introduces novel lower bounds on the essential dimension of finite groups using techniques from birational geometry.

Findings

New lower bounds on essential dimension for specific finite groups

Application of birational geometry to group theory problems

Improved understanding of Cremona groups' properties

Abstract

We use a recent advance in birational geometry to prove new lower bounds on the essential dimension of some finite groups.