Sur la simplicité et la stabilité du fibré tangent des variétés rationelles homogènes Soit G/P une variété homogène rationnelle, où G est un groupe de Lie simple, complexe et de type ADE. On démontre que le fibré tangent T_G/P est simple, c'est-à-dire, ses seuls endomorphismes sont les multiples scalaires de l'identité. Notre théorème, combiné avec la correspondance de Hitchin-Kobayashi, implique la stabilité du fibré tangent par rapport à la polarisation anticanonique. L'instrument principal qu'on utilise est l'équivalence des catégories des fibrés vectoriels homogènes sur G/P et des représentations de dimension finie d'un carquois avec relations introduit par Bondal et Kapranov in 1990.

Given a rational homogeneous variety G/P where G is complex simple and of type ADE, we prove that the tangent bundle _G/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.

On simplicity and stability of tangent bundles of rational homogeneous varieties

Boralevi, Ada
2012-01-01

Abstract

Given a rational homogeneous variety G/P where G is complex simple and of type ADE, we prove that the tangent bundle _G/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.
2012
Geometric Methods in Representation Theory
24
II
273
295
978-2-85629-361-4
Boralevi, Ada
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/33403
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