On simplicity and stability of tangent bundles of rational homogeneous varieties
Ada Boralevi

TL;DR
This paper proves that tangent bundles of rational homogeneous varieties of type ADE are simple and stable, using quiver representations and the Hitchin-Kobayashi correspondence, advancing understanding of their geometric and algebraic properties.
Contribution
It establishes the simplicity and stability of tangent bundles on G/P for type ADE, linking homogeneous vector bundles to quiver representations.
Findings
All tangent bundles T_{G/P} are simple.
Tangent bundles are stable with respect to the anticanonical polarization.
Utilizes quiver category equivalence to prove main results.
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry
