On simplicity and stability of tangent bundles of rational homogeneous varieties

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Boralevi, Ada
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Abstract
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Given a rational homogeneous variety G/P where G is complex simple and of type ADE, we prove that all tangent bundles T_{G/P} are simple, meaning that their only endomorphisms are scalar multiples of the identity. This result combined with Hitchin-Kobayashi correspondence implies stability of these tangent bundles 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.
Comment: Part of the author's PhD thesis, 3 figures
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Mathematics - Algebraic Geometry, Mathematics - Representation Theory, 14F05, 14M17, 14D20, 16G20
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