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Principal bundles whose restrictions to a curve are isomorphic

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Let X be a normal projective variety defined over an algebraically closed field k. Let |O X (1)| be a very ample invertible sheaf on X. Let G be an affine algebraic group defined over k. Let E G and F G be two principal G-bundles on X. Then there exists an integer n > > 0 (depending on E G and F G ) such that if the restrictions of E G and F G to a curve C ∈ |O X (n)| are isomorphic, then they are isomorphic on all of X.

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  1. School of Mathematics, Tata Institute of Fundamental Research, Dr Homi Bhabha Road, Mumbai, 400 005, India

    SUDARSHAN RAJENDRA GURJAR

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  1. SUDARSHAN RAJENDRA GURJAR
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Correspondence to SUDARSHAN RAJENDRA GURJAR.

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GURJAR, S.R. Principal bundles whose restrictions to a curve are isomorphic. Proc Math Sci 121, 165–170 (2011). https://doi.org/10.1007/s12044-011-0008-9

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  • DOI: https://doi.org/10.1007/s12044-011-0008-9

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