A new presentation of the plane Cremona group
Christian Urech, Susanna Zimmermann

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.
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