Soient un groupe algébrique simple et sa compactification magnifique. Nous montrons que 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 , lorsque n’est pas de type ou .
Consider a simple algebraic group of adjoint type, and its wonderful compactification . We show that 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 has the target rigidity property when is not of type or .
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@article{JEP_2015__2__153_0,
author = {Michel Brion and Baohua Fu},
title = {Minimal rational curves on wonderful~group~compactifications},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {153--170},
publisher = {\'Ecole polytechnique},
volume = {2},
year = {2015},
doi = {10.5802/jep.20},
mrnumber = {3370091},
zbl = {1348.14124},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.20/}
}
TY - JOUR AU - Michel Brion AU - Baohua Fu TI - Minimal rational curves on wonderful group compactifications JO - Journal de l’École polytechnique — Mathématiques PY - 2015 SP - 153 EP - 170 VL - 2 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.20/ DO - 10.5802/jep.20 LA - en ID - JEP_2015__2__153_0 ER -
%0 Journal Article %A Michel Brion %A Baohua Fu %T Minimal rational curves on wonderful group compactifications %J Journal de l’École polytechnique — Mathématiques %D 2015 %P 153-170 %V 2 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.20/ %R 10.5802/jep.20 %G en %F JEP_2015__2__153_0
Michel Brion; Baohua Fu. 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/articles/10.5802/jep.20/
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