Minimal rational curves on wonderful group compactifications
Journal de l’École polytechnique — Mathématiques, Volume 2 (2015), pp. 153-170.

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.

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.

DOI: 10.5802/jep.20
Classification: 14L30, 14M27, 20G20
Keywords: Minimal rational curves, wonderful compactifications
Mot clés : Courbes rationnelles minimales, compactifications magnifiques
Brion, Michel 1; Fu, Baohua 2

1 Institut Fourier, Université de Grenoble B.P. 74, 38402 Saint-Martin d’Hères Cedex, France
2 Institute of Mathematics, AMSS 55 ZhongGuanCun East Road, Beijing, 100190, China
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Brion, Michel; Fu, Baohua. Minimal rational curves on wonderful group compactifications. Journal de l’École polytechnique — Mathématiques, Volume 2 (2015), pp. 153-170. doi : 10.5802/jep.20. http://www.numdam.org/articles/10.5802/jep.20/

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