Elements and cyclic subgroups of finite order of the Cremona group

TL;DR

This paper classifies elements and cyclic subgroups of finite order in the Cremona group, providing parametrizations of conjugacy classes linked to fixed curves of positive genus, advancing understanding of the group's structure.

Contribution

It offers a complete classification of finite order elements and cyclic subgroups in the Cremona group, with natural parametrizations based on fixed curves.

Findings

Classification of finite order elements and subgroups in the Cremona group

Parametrizations of conjugacy classes related to fixed curves of positive genus

Enhanced understanding of the structure of the Cremona group

Abstract

We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.