Transformations birationnelles quadratiques de l'espace projectif complexe à trois dimensions
Annales de l'Institut Fourier, Tome 51 (2001) no. 5, pp. 1153-1187.

Nous classifions les transformations birationnelles quadratiques de l'espace projectif complexe de dimension trois, à des isomorphismes linéaires près. Elles sont de trois sortes, selon que le degré de leur inverse est 2, 3 ou 4. Il y a en tout 30 types différents; en 1871, L. Cremona en avait déjà décrit 23.

We classify birational quadratic transformations of the three dimensional complex projective space, up to linear isomorphisms of source and target. They are of three kinds, depending on the degree of the inverse, which can be 2,3 or 4. There are 30 different types; in 1871, L. Cremona described 23 of them already.

DOI : https://doi.org/10.5802/aif.1850
Classification : 14E07
Mots clés : quadriques, transformations birationnelles
@article{AIF_2001__51_5_1153_0,
     author = {Pan, Ivan and Ronga, Felice and Vust, Thierry},
     title = {Transformations birationnelles quadratiques de l'espace projectif complexe \`a trois dimensions},
     journal = {Annales de l'Institut Fourier},
     pages = {1153--1187},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     doi = {10.5802/aif.1850},
     zbl = {0987.14009},
     mrnumber = {1860661},
     language = {fr},
     url = {archive.numdam.org/item/AIF_2001__51_5_1153_0/}
}
Pan, Ivan; Ronga, Felice; Vust, Thierry. Transformations birationnelles quadratiques de l'espace projectif complexe à trois dimensions. Annales de l'Institut Fourier, Tome 51 (2001) no. 5, pp. 1153-1187. doi : 10.5802/aif.1850. http://archive.numdam.org/item/AIF_2001__51_5_1153_0/

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