Restricted Lazarsfeld-Mukai bundles and canonical curves

@article{Aprodu2014RestrictedLB,
  title={Restricted Lazarsfeld-Mukai bundles and canonical curves},
  author={Marian Aprodu and Gavril Farkas and Angela Ortega},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
We prove two results. First, we establish that the normal bundle of any smooth curve of genus 7 having maximal Clifford index is stable. Note that 7 is the smallest genus for which such a result could possibly hold. We then show that rank four Lazarsfeld-Mukai vector bundles on a curve that lies on a general K3 surface are stable. Both results have consequences for Mercat's conjecture on higher rank vector bundles on generic curves. 
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