Minimal rational curves on wonderful group compactifications
[Courbes rationnelles minimales sur les compactifications magnifiques des groupes]
Journal de l’École polytechnique — Mathématiques, Tome 2 (2015) , pp. 153-170.

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.

Reçu le : 2015-04-08
Accepté le : 2015-06-17
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 = {Michel Brion and Baohua Fu},
     title = {Minimal rational curves on wonderful~group~compactifications},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     pages = {153--170},
     publisher = {\'Ecole polytechnique},
     volume = {2},
     year = {2015},
     doi = {10.5802/jep.20},
     zbl = {1348.14124},
     mrnumber = {3370091},
     language = {en},
     url = {jep.centre-mersenne.org/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. https://jep.centre-mersenne.org/item/JEP_2015__2__153_0/

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