• Vector bundles as direct images of line bundles

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    • Keywords


      Projective variety; algebraic vector bundle; line bundle; direct image; finite morphism

    • Abstract


      LetX be a smooth irreducible projective variety over an algebraically closed fieldK andE a vector bundle onX. We prove that, if dimX ≥ 1, there exist a smooth irreducible projective varietyZ overK, a surjective separable morphismf:ZX which is finite outside an algebraic subset of codimension ≥ 3 inX and a line bundleL onX such that the direct image ofL byf is isomorphic toE. WhenX is a curve, we show thatZ, f, L can be so chosen thatf is finite and the canonical mapH1(Z, O) →H1(X, EndE) is surjective.

    • Author Affiliations


      A Hirschowitz1 M S Narasimhan1 2

      1. Université de Nice Sophia-Antipolis, Parc Valrose, Nice Cedex 2 - 06108, France
      2. International Centre for Theoretical Physics, P.O. Box 586, Trieste - 34100, Italy
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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