The Green conjecture for exceptional curves on a $K3$ surface. Aprodu, M. & Pacienza, G. Int. Math. Res. Not. IMRN, 2008.
The Green conjecture for exceptional curves on a $K3$ surface [link]Paper  doi  bibtex   
@Article{	  apr.pac:08,
  author	= {Aprodu, Marian and Pacienza, Gianluca},
  title		= {The {G}reen conjecture for exceptional curves on a {$K3$}
		  surface},
  journal	= {Int. Math. Res. Not. IMRN},
  fjournal	= {International Mathematics Research Notices. IMRN},
  year		= {2008},
  number	= {14},
  pages		= {Art. ID rnn043, 25},
  issn		= {1073-7928},
  doi		= {10.1093/imrn/rnn043},
  url		= {http://dx.doi.org/10.1093/imrn/rnn043}
}

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