Minimal rational curves on wonderful group compactifications

Brion, Michel; Fu, Baohua

Minimal rational curves on wonderful group compactifications
[Courbes rationnelles minimales sur les compactifications magnifiques des groupes]

Brion, Michel ; Fu, Baohua

Journal de l'École polytechnique - Mathématiques, Tome 2 (2015), p. 153-170 / Harvested from Numdam

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Résumé
Abstract

Soient $G$ un groupe algébrique simple et $X$ sa compactification magnifique. Nous montrons que $X$ possède une unique famille de courbes rationnelles minimales, et nous décrivons explicitement la sous-famille formée des courbes passant par un point général. Nous en déduisons une propriété de rigidité de $X$ , lorsque $G$ n’est pas de type $A_{1}$ ou $C$ .

Consider a simple algebraic group $G$ of adjoint type, and its wonderful compactification $X$ . We show that $X$ admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an application, we show that $X$ has the target rigidity property when $G$ is not of type $A_{1}$ or $C$ .

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/jep.20
Classification: 14L30, 14M27, 20G20
Mots clés: Courbes rationnelles minimales, compactifications magnifiques

@article{JEP_2015__2__153_0,
     author = {Brion, Michel and Fu, Baohua},
     title = {Minimal rational curves on wonderful~group~compactifications},
     journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
     volume = {2},
     year = {2015},
     pages = {153-170},
     doi = {10.5802/jep.20},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEP_2015__2__153_0}
}

Brion, Michel; Fu, Baohua. Minimal rational curves on wonderful group compactifications. Journal de l'École polytechnique - Mathématiques, Tome 2 (2015) pp. 153-170. doi : 10.5802/jep.20. http://gdmltest.u-ga.fr/item/JEP_2015__2__153_0/

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