On simplicity and stability of tangent bundles of rational homogeneous varieties - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: Given a rational homogeneous variety G-P where G is complex simple and oftype ADE, we prove that all tangent bundles T {G-P} are simple, meaning thattheir only endomorphisms are scalar multiples of the identity. This resultcombined with Hitchin-Kobayashi correspondence implies stability of thesetangent bundles with respect to the anticanonical polarization. Our main toolis the equivalence of categories between homogeneous vector bundles on G-P andfinite dimensional representations of a given quiver with relations.



Author: Ada Boralevi

Source: https://arxiv.org/







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