Transformations birationnelles quadratiques de l'espace projectif complexe à trois dimensions  [ Birational quadratic transformations of the three dimensional complex projective space ]
Annales de l'Institut Fourier, Volume 51 (2001) no. 5, p. 1153-1187

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.

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.

DOI : https://doi.org/10.5802/aif.1850
Classification:  14E07
Keywords: quadrics, birational transformations
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     pages = {1153-1187},
     doi = {10.5802/aif.1850},
     zbl = {0987.14009},
     mrnumber = {1860661},
     language = {fr},
     url = {http://www.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, Volume 51 (2001) no. 5, pp. 1153-1187. doi : 10.5802/aif.1850. http://www.numdam.org/item/AIF_2001__51_5_1153_0/

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