GIT ones and quivers

Eugène Bataillon

Description

Niveau: Supérieur, Doctorat, Bac+8
GIT- ones and quivers N. Ressayre ? June 8, 2009 Abstra t In this work, we improve results of [Res07, Res08a? about GIT- ones asso iated to the a tion of a redu tive group G on a proje tive variety X . These results are applied to give a short proof of the Derksen- Weyman theorem whi h parametrizes bije tively the fa es of a rational one asso iated to any quiver without oriented y le. An important example of su h a one is the Horn one. Contents 1 Introdu tion 2 2 Well overing pairs and GIT- ones 3 2.1 Well overing pairs . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Total ones and well overing pair . . . . . . . . . . . . . . . . 4 3 Appli ation to quiver representations 8 3.1 Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Three ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Dominant pairs . . .

• linear group


• let


• lx ?t ?


• group


• g?-linearized line bundles


• tion morphism


• picg ?


• derksen-weyman theorem

Sujets

• Université Montpellier 2
• Bataillon
• Matrix group

Informations

• Publié par: mijec
• Nombre de lectures: 23
• Langue: English

Extrait

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