Mathematische Annalen

, Volume 338, Issue 3, pp 627–667 | Cite as

Déformations des cônes de vecteurs primitifs

Article

Mathematics Subject Classification (2000)

14B07 14L30 14M17 17C20 20G05 

Résumé

Pour un groupe réductif connexe complexe G, on classifie les modules simples dont le cône des vecteurs primitifs admet une déformation G-invariante non triviale. On relie cette classification à celle (due à Akhiezer) des variétés projectives lisses dont les orbites sous l’action d’un groupe algébrique affine connexe sont un diviseur et son complémentaire.

Notre principal outil est le schéma de Hilbert invariant d’Alexeev et Brion; on en détermine les premiers exemples.

On détermine aussi les déformations infinitésimales (non nécessairement G-invariantes) des cônes des vecteurs primitifs; elles sont triviales pour presque tous les modules simples.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institut de Mathématiques et de Modélisation de Montpellier, UMR CNRS 5149Université de Montpellier IIMontpellierFrance

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