Les transformations de Cremona stellaires
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- by Ivan Pan PDF
- Proc. Amer. Math. Soc. 129 (2001), 1257-1262 Request permission
Abstract:
On construit explicitement toutes les transformations de Cremona de $\mathbf {P}^{n}$ qui satisfont à la propriété suivante: il existe $P_{1},P_{2}\in \mathbf {P}^{n}$ tels que les droites par $P_{1}$ sont envoyées sur les droites par $P_{2}$. On caractérise de plusieurs manières ces transformations et pour chaque entier non-négatif $d$ on donne des formules pour la dimension de l’ensemble constitué de celles qui ont degré $d$.
Abstract. We construct the Cremona transformations of $\mathbf {P}^{n}$ satisfying the following property: there exist $P_{1},P_{2}\in \mathbf {P}^{n}$ such that the image of all straight lines through $P_{1}$ are straight lines through $P_{2}$. We characterise these transformations, and for all non-negative integer $d$ we give a formula for the dimension of the set of those whose degree is $d$.
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Additional Information
- Ivan Pan
- Affiliation: Instituto de Matemática-UFRGS, av. Bento Gonçalves 9500, 91540-000 Porto Alegre/RS, Brasil
- Email: pan@mat.ufrgs.br
- Received by editor(s): July 20, 1999
- Published electronically: October 12, 2000
- Additional Notes: Au moment de la redaction de ce travail, l’auteur était attaché à l’Instituto de Matemática-UFRGS en qualité de boursier du CNPq-Brésil
- Communicated by: Michael Stillman
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1257-1262
- MSC (1991): Primary 14E07, 14N99
- DOI: https://doi.org/10.1090/S0002-9939-00-05749-X
- MathSciNet review: 1814153