A new presentation of the plane Cremona group

TL;DR

This paper provides a simplified and explicit presentation of the plane Cremona group over an algebraically closed field, based on classical generators, facilitating calculations in algebraic geometry.

Contribution

It introduces a new, simpler presentation of the plane Cremona group using classical generators, improving computational accessibility.

Findings

Simplified presentation of the Cremona group

Explicit generators based on Noether and Castelnuovo theorems

Facilitates calculations in algebraic geometry

Abstract

We give a presentation of the plane Cremona group over an algebraically closed field with respect to the generators given by the Theorem of Noether and Castelnuovo. This presentation is particularly simple and can be used for explicit calculations.