Les transformations de Cremona stellaires. (The stellar Cremona transformations) (Q2701616)

The author studies birational transformations \(F\) of \({\mathbb P}^n\) with the following property: There are points \(P,Q\in {\mathbb P}^n\) such that \(F\) induces a birational transformation between the set of lines through \(P\) and the set of lines through \(Q\). The group St of these stellar transformations with fixed \(P=Q\) fits in an exact sequence: NEWLINE\[NEWLINE1 \to PGL(2,K(y_1,\dots,y_{n-1}))\to\text{St}\to \text{Cr}({\mathbb P}^{n-1})\to 1NEWLINE\]NEWLINE The author describes the elements of St in terms of their image in the group \(\text{Cr}({\mathbb P}^{n-1})\) of Cremona transformations of \({\mathbb P}^{n-1}\). With this description, the author computes the dimension of subgroups of St whose image is a fixed subgroup of \(\text{Cr}({\mathbb P}^{n-1})\).