Principal bundles whose restriction to curves are trivial |
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Authors: | Indranil Biswas Yogish I Holla |
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Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400005, India |
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Abstract: | Let k be an algebraically closed field and X a smooth projective variety defined over k. Let EG be a principal G–bundle over X, where G is an algebraic group defined over k, with the property that for every smooth curve C in X the restriction of EG to C is the trivial G–bundle. We prove that the principal G–bundle EG over X is trivial. We also give examples of nontrivial principal bundle over a quasi-projective variety Y whose restriction to every smooth curve in Y is trivial. |
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