On simplicity and stability of tangent bundles of rational homogeneous varieties
Résumé
Given a rational homogeneous variety G/P where G is complex simple and of type ADE, we prove that the tangent bundle TG/P is simple, meaning that its only endomorphisms are scalar multiples of the identity. This result combined with Hitchin-Kobayashi correspondence implies stability of the tangent bundle with respect to the anticanonical polarization. Our main tool is the equivalence of categories between homogeneous vector bundles on G/P and finite dimensional representations of a given quiver with relations.
Origine : Fichiers produits par l'(les) auteur(s)
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