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Sur la structure locale des variétés sphériques. (On the local structure of spherical varieties). (French) Zbl 0656.14028

Es seien G eine zusammenhängende reduktive algebraische Gruppe über einem algebraisch abgeschlossenen Körper der Charakteristik 0, T ein maximaler Torus von G und X eine sphärische G-Varietät (d.h. X ist normal und eine Boreluntergruppe von G hat eine dichte Bahn in X). Die Autoren beschreiben die lokale Struktur von X in der Umgebung eines Fixpunktes von T.
Damit können einige Eigenschaften von Toruseinbettungen auf eine Klasse von gewissen (“toroidalen”) sphärischen G-Varietäten übertragen werden. Als weitere Anwendung wird eine durch die T-Operation definierte Zellzerlegung von vollständigen sphärischen toroidalen G-Varietäten beschrieben.
Reviewer: F.Pauer

MSC:

14L30 Group actions on varieties or schemes (quotients)
14J25 Special surfaces
14M17 Homogeneous spaces and generalizations
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References:

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