On the vector bundles over rationally connected varieties

Biswas, Indranil ; dos Santos, Joao Pedro P. (2009) On the vector bundles over rationally connected varieties Comptes Rendus Mathematique, 347 (19-20). pp. 1173-1176. ISSN 1631-073X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S16310...

Related URL: http://dx.doi.org/10.1016/j.crma.2009.09.006

Abstract

Let X be a rationally connected smooth projective variety defined over C and E →X a vector bundle such that for every morphism γ :CP1 → X , the pullback γ E is trivial. We prove that E is trivial. Using this we show that if γ E is isomorphic to L(γ) ⊕r for all γ of the above type, where L(γ) → CP1 is some line bundle, then there is a line bundle ζ over X such that E=ζ⊕r.

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Deposited On:12 Oct 2010 04:17
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