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Journal of the Ramanujan Mathematical Society

Volume 28, Issue 4, December 2013  pp. 423–442.

Triviality criteria for bundles over rationally connected varieties

Authors Indranil Biswas and João Pedro Dos Santos
Author institution: School of Mathematics, Tata Institute of Fundamental Research, Homi BhabhaRoad, Bombay 400 005, India

Summary:  Let X be a separably rationally connected smooth projective variety defined over an algebraically closed field K. If E → X is a vector bundle satisfying the condition that for every morphism γ : PK1 → X the pull-back γ*E is trivial, we prove that E is trivial. If E → X is a strongly semistable vector bundle such that c1(E) and c2(E) are numerically equivalent to zero, we prove that E is trivial. We also show that X does not admit any nontrivial stratified sheaf. These results are also generalized to principal bundles over X.

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