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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Ce travail a été partiellement soutenu par le réseau Liegrits MRTN-CT 2003-505078.