Geodesic
On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 531-544 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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We consider a smooth projective variety $X$ on which a simple algebraic group $G$ acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of $G$ with the induced action of $G$ on the normal bundle of a closed orbit of the action. We get effective results in case $G=SL(n)$ and $\dim X \leq 2n-2$. 
@article{BUMI_2003_8_6B_3_a1,
     author = {Andreatta, Marco and Wi\'sniewski, Jaros{\l}aw A.},
     title = {On quasihomogeneous manifolds {\textendash} via {Brion-Luna-Vust} theorem},
     journal = {Bollettino della Unione matematica italiana},
     pages = {531--544},
     year = {2003},
     volume = {Ser. 8, 6B},
     number = {3},
     zbl = {1178.14047},
     mrnumber = {MR2014816},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a1/}
}
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Andreatta, Marco; Wiśniewski, Jarosław A. On quasihomogeneous manifolds – via Brion-Luna-Vust theorem. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 531-544. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a1/