Mukai's program for curves on a K3 surface

@article{Arbarello2013MukaisPF,
  title={Mukai's program for curves on a K3 surface},
  author={Enrico Arbarello and Andrea Bruno and Edoardo Sernesi},
  journal={arXiv: Algebraic Geometry},
  year={2013}
}
Let C be a general element in the locus of curves in M_g lying on some K3 surface, where g is congruent to 3 mod 4 and greater than or equal to 15. Following Mukai's ideas, we show how to reconstruct the K3 surface as a Fourier-Mukai transform of a Brill-Noether locus of rank two vector bundles on C. 
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