On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
Andreatta, Marco ; Wiśniewski, Jarosław A.
Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 531-544 / Harvested from 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=S⁢L⁢n and dim⁡X≤2⁢n-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=S⁢L⁢n e dim⁡X≤2⁢n-2.

Publié le : 2003-10-01
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     author = {Marco Andreatta and Jaros\l aw A. Wi\'sniewski},
     title = {On quasihomogeneous manifolds -- via Brion-Luna-Vust theorem},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {6-A},
     year = {2003},
     pages = {531-544},
     zbl = {1178.14047},
     mrnumber = {2014816},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_3_531_0}
}

Andreatta, Marco; Wiśniewski, Jarosław A. On quasihomogeneous manifolds – via Brion-Luna-Vust theorem. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 531-544. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_3_531_0/

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