Algebraic elements of the Cremona groups

TL;DR

This paper investigates algebraic elements within the Cremona group, revealing that while they form a countable union of closed sets, this set is not closed, highlighting complex topological properties.

Contribution

It provides a detailed analysis of the topological structure of algebraic elements in the Cremona group, a topic not thoroughly explored before.

Findings

Algebraic elements form a countable union of closed subsets.

The set of algebraic elements is not closed.

The study advances understanding of Cremona group topology.

Abstract

This article studies algebraic elements of the Cremona group. In particular, we show that the set of all these elements is a countable union of closed subsets but it is not closed.