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Les transformations de Cremona stellaires. (The stellar Cremona transformations). (French) Zbl 0966.14009
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: $1 \to PGL(2,K(y_1,\dots,y_{n-1}))\to\text{St}\to \text{Cr}({\mathbb P}^{n-1})\to 1$ 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 $$\text{Cr}({\mathbb P}^{n-1})$$.

##### MSC:
 14E07 Birational automorphisms, Cremona group and generalizations 14N99 Projective and enumerative algebraic geometry 14E05 Rational and birational maps
##### Keywords:
Cremona transformations; stellar transformations
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##### References:
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