Triviality and Split of Vector Bundles on Rationally Connected Varieties

Abstract

In this paper, we give a simple proof of a triviality criterion due to I.Biswas and J.Pedro and P.Dos Santos. We also prove a vector bundle on a homogenous space is trivial if and only if the restrictions of the vector bundle to Schubert lines are trivial. Using this result and Chern classes of vector bundles, we give a general criterion of a uniform vector bundle on a homogenous space to be splitting. As an application, we prove a uniform vector bundle on classical Grassmannians and quadrics of low rank is splitting.

(submitted) 13 pages, 1 figure

References in corpus (3)

• The connectedness of the moduli space of maps to homogeneous spaces
• Fano Hypersurfaces in Positive Characteristic
• Looking for rational curves on cubic hypersurfaces