## Birational quadratic transformations of the three dimensional complex projective space. (Transformations birationnelles quadratiques de l’espace projectif complexe à trois dimensions.)(French)Zbl 0987.14009

The paper concerns the classical subject of the classification of all birational morphisms (i.e. Cremona transformations) of $$\mathbb P^n(\mathbb C)$$ in particular case $$n=3$$ and degree of morphisms 2. The main result is a finite list of birational morphisms of $$\mathbb P^3(\mathbb C)$$ of degree 2 (a geometric description of them is also given) such that any other birational morphism $$\phi :\mathbb P^3_x(\mathbb C) \to \mathbb P^3_y(\mathbb C)$$ of degree 2 is equal to one in this list up to linear changes of variables in $$\mathbb P^3_x(\mathbb C)$$ and $$\mathbb P^3_y(\mathbb C)$$. Besides, the authors divide the whole class of birational morphisms of degree 2 in three natural subclasses (non-disjoint) which are locally closed subvarieties in an appropriate Grassmannian.

### MSC:

 1.4e+08 Birational automorphisms, Cremona group and generalizations

### Keywords:

birational morphism; Cremona group
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### References:

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