Geodesic
On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 531-544.

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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 $\dim X \leq 2n-2$.
In questo lavoro si studiano varietà proiettive liscie sulle quali agisce un gruppo algebrico semplice $G$ con una orbita aperta. In particolare si utilizza un teorema di Brion-Luna-Vust per correlare l'azione di $G$ su $X$ con l'azione indotta di $G$ sul fibrato normale di una orbita chiusa. Come applicazione si ottiene una classificazione nel caso $G=SL(n)$ e $\dim X \leq 2n-2$. 
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     title = {On quasihomogeneous manifolds {\textendash} via {Brion-Luna-Vust} theorem},
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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/

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