Proceedings Mathematical Sciences

, Volume 104, Issue 1, pp 191–200 | Cite as

Vector bundles as direct images of line bundles

  • A. Hirschowitz
  • M. S. Narasimhan
Obituary note


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 mapH 1(Z, O) →H 1(X, EndE) is surjective.


Projective variety algebraic vector bundle line bundle direct image finite morphism 


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Copyright information

© Indian Academy of Science 1994

Authors and Affiliations

  • A. Hirschowitz
    • 1
  • M. S. Narasimhan
    • 1
    • 2
  1. 1.Université de Nice Sophia-AntipolisNice Cedex 2France
  2. 2.International Centre for Theoretical PhysicsTriesteItaly

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