On simplicity and stability of tangent bundles of rational homogeneous varieties

Details On simplicity and stability of tangent bundles of rational homogeneous varieties On simplicity and stability of tangent bundles of rational homogeneous varieties

2009-01-15

arxiv.org/abs/0901.2350v1

Mathematics

Algebraic Geometry

Part of the author's PhD thesis, 3 figures

Scientific paper

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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