On the conjugacy classes of monomial birational maps

TL;DR

This paper investigates the structure of conjugacy classes within the group of monomial birational maps in higher-dimensional Cremona groups, providing insights into their classification and properties.

Contribution

It offers a new analysis of conjugacy classes for monomial birational maps in dimensions two and higher, advancing understanding of their algebraic structure.

Findings

Characterization of conjugacy classes in monomial birational maps

Identification of invariants under conjugation

Insights into the structure of the Cremona group

Abstract

This short note deals with the conjugacy classes of monomial birational maps in the $n$-dimensional Cremona group, $n\geq 2$.