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arXiv · 0901.2350

On simplicity and stability of tangent bundles of rational homogeneous varieties

Ada Boralevi
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Abstract

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.

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Ada Boralevi. 2009-01-15. On simplicity and stability of tangent bundles of rational homogeneous varieties. https://arxiv.org/abs/0901.2350

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