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Direct images of vector bundles and connections

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Abstract

Let E be a vector bundle over an irreducible projective variety X defined over an algebraically closed field. We give a necessary and sufficient condition for E to be a direct image of a vector bundle on an étale cover, of degree more than one, of X. In fact, we describe all possible ways E can be realized as a direct image. Given a connection D on E, a criterion is given for D to be induced by a connection on a vector bundle whose direct image, by an étale covering map of degree more than one, is E.

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Acknowledgements

The first-named author is supported by a J. C. Bose Fellowship. The last-named author was supported by SFB/TR 45 “Periods, moduli and arithmetic of algebraic varieties”, subproject M08-10 “Moduli of vector bundles on higher-dimensional varieties”.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    Indranil Biswas & Chandranandan Gangopadhyay

  2. Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann-Str. 9, 45127, Essen, Germany

    Michael Lennox Wong

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  1. Indranil Biswas
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  2. Chandranandan Gangopadhyay
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  3. Michael Lennox Wong
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Correspondence to Indranil Biswas.

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Biswas, I., Gangopadhyay, C. & Wong, M.L. Direct images of vector bundles and connections. Beitr Algebra Geom 60, 137–156 (2019). https://doi.org/10.1007/s13366-018-0410-x

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  • DOI: https://doi.org/10.1007/s13366-018-0410-x

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