Spectral curves and the generalised theta divisor.

  title={Spectral curves and the generalised theta divisor.},
  author={Arnaud Beauville and S. Ramanan and M. S. Narasimhan},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={169 - 179}
Let X be a smooth, irreducible, projective curve over an algebraically closed field of characteristic 0 and let g = gx ̂ 2 be its genus. We show in this paper that a generic vector b ndle on X of rank n and any fixed degree can be obtained s the direct image of a line b ndle on an n-sheeted (ramified) covering of X. From this we deduce results concerning linear Systems on the moduli space of vector bundles of rank n and degree 0. 
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