Hirschowitz, A. ; Narasimhan, M. S. (1994) Vector bundles as direct images of line bundles Proceedings of the Indian Academy of Sciences  Mathematical Sciences, 104 (1). pp. 191200. ISSN 02534142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/104/1/1912...
Related URL: http://dx.doi.org/10.1007/BF02830882
Abstract
Let X be a smooth irreducible projective variety over an algebraically closed field K and E a vector bundle on X. We prove that, if dim X≥1, there exist a smooth irreducible projective variety Z over K, a surjective separable morphism f:Z →X which is finite outside an algebraic subset of codimension ≥3 in X and a line bundle L on X such that the direct image of L by f is isomorphic to E. When X is a curve, we show that Z, f, L can be so chosen that f is finite and the canonical map H^{1}(Z, O) →H^{1}(X, End E) is surjective.
Item Type:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Projective Variety; Algebraic Vector Bundle; Line Bundle; Direct Image; Finite Morphism 
ID Code:  58109 
Deposited On:  31 Aug 2011 12:29 
Last Modified:  18 May 2016 09:14 
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