This article studies the group generated by automorphisms of the projective space of dimension and by the standard birational involution of degree . Every element of this group only contracts rational hypersurfaces, but in odd dimension, there are simple elements having this property which do not belong to the group. Geometric properties of the elements of the group are given, as well as a description of its intersection with monomial transformations.
Cet article étudie le groupe engendré par les automorphismes de l’espace projectif de dimension et par l’involution birationnelle standard de degré . Tout élément de ce groupe ne contracte que des hypersurfaces rationnelles, mais en dimension impaire il existe des éléments simples qui ont cette propriété et n’appartiennent pas au groupe. Des propriétés géométriques du groupe sont données, de même qu’une description de son intersection avec le groupe des transformations monômiales.
Revised:
Accepted:
Published online:
Classification: 14E07
Keywords: Cremona transformation, standard involution, rational hypersurfaces, monomial transformations
@article{AIF_2015__65_6_2641_0, author = {Blanc, J\'er\'emy and Hed\'en, Isac}, title = {The group of {Cremona} transformations generated by linear maps and the standard involution}, journal = {Annales de l'Institut Fourier}, pages = {2641--2680}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {6}, year = {2015}, doi = {10.5802/aif.2999}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2999/} }
TY - JOUR TI - The group of Cremona transformations generated by linear maps and the standard involution JO - Annales de l'Institut Fourier PY - 2015 DA - 2015/// SP - 2641 EP - 2680 VL - 65 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2999/ UR - https://doi.org/10.5802/aif.2999 DO - 10.5802/aif.2999 LA - en ID - AIF_2015__65_6_2641_0 ER -
%0 Journal Article %T The group of Cremona transformations generated by linear maps and the standard involution %J Annales de l'Institut Fourier %D 2015 %P 2641-2680 %V 65 %N 6 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.2999 %R 10.5802/aif.2999 %G en %F AIF_2015__65_6_2641_0
Blanc, Jérémy; Hedén, Isac. The group of Cremona transformations generated by linear maps and the standard involution. Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2641-2680. doi : 10.5802/aif.2999. https://aif.centre-mersenne.org/articles/10.5802/aif.2999/
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