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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Les transformations de Cremona stellaires


Author: Ivan Pan
Journal: Proc. Amer. Math. Soc. 129 (2001), 1257-1262
MSC (1991): Primary 14E07, 14N99
Published electronically: October 12, 2000
MathSciNet review: 1814153
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05749-X
PII: S 0002-9939(00)05749-X
Keywords: Transformation de Cremona, stellaire
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
Article copyright: © Copyright 2000 American Mathematical Society