Combinatorics of affine birational maps

Abstract

The main object of study of the present paper is the group $\au_n$ of \emph{unimodular automorphisms} of $\com^n$. Taking $\au_n$ as a working example, our intention was to develop an approach (or rather an edifice) which allows one to prove, for instance, the non-simplicity of $\au_n$ for all $n\ge 3$. More systematic and, perhaps, general exposition will appear elsewhere.

13 pages, 1 figure; v5: minor changes

References in corpus (3)

• Simple finite subgroups of the Cremona group of rank 3
• Normal subgroups in the Cremona group (long version)
• Transformations birationnelles de petit degré