Five embeddings of one simple group

TL;DR

This paper introduces a new approach using multiplier ideal sheaves to study birational maps between Fano varieties, proving rigidity results and identifying multiple non-conjugate subgroups of the Cremona group related to A6.

Contribution

It develops a novel method for analyzing birational maps and demonstrates the existence of multiple non-conjugate A6 subgroups in the Cremona group of rank 3.

Findings

Proves equivariant birational rigidity of four Fano threefolds with A6 action

Establishes at least five non-conjugate A6 subgroups in the Cremona group of rank 3

Introduces a new technique based on multiplier ideal sheaves for birational geometry

Abstract

We propose a new method to study birational maps between Fano varieties based on multiplier ideal sheaves. Using this method, we prove equivariant birational rigidity of four Fano threefolds acted on by the group A6. As an application, we obtain that the Cremona group of rank 3 has at least five non-conjugate subgroups isomorphic to A6.