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arXiv · 1310.5774

Triviality and Split of Vector Bundles on Rationally Connected Varieties

Xuanyu Pan
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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.

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Xuanyu Pan. 2014-02-07. Triviality and Split of Vector Bundles on Rationally Connected Varieties. https://arxiv.org/abs/1310.5774

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