The Cremona group is compactly presentable
Susana Zimmermann

TL;DR
This paper proves that the Cremona group, a fundamental object in algebraic geometry, has a compact presentation by expressing it as a generalized amalgamated product of specific algebraic subgroups with a single defining relation.
Contribution
It establishes the first known compact presentation of the Cremona group, revealing its structure as a generalized amalgamated product divided by one relation.
Findings
Cremona group is a generalized amalgamated product of three algebraic subgroups.
The group admits a compact presentation with a single relation.
The structure simplifies understanding of Cremona group's algebraic properties.
Abstract
This article shows that the Cremona group is compactly presentable. To prove this we show that it is a generalised amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one relation.
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