PROJECTIVE NORMALITY OF ALGEBRAIC CURVES AND ITS APPLICATION TO SURFACES

@article{Kim2006PROJECTIVENO,
  title={PROJECTIVE NORMALITY OF ALGEBRAIC CURVES AND ITS APPLICATION TO SURFACES},
  author={Seonja Kim and Young-Rock Kim},
  journal={Osaka Journal of Mathematics},
  year={2006},
  volume={44},
  pages={685-690}
}
Let L be a very ample line bundle on a smooth curve C of genus g with (3g + 3) 2 deg L 2g 5. Then L is normally generated if deg L max 2g + 2 4h 1 (C, L), 2g (g 1) 6 2h 1 (C, L) . Let C be a triple covering of genus p curve C with C C and D a divisor on C with 4 p deg D (g 1) 6 2 p. Then KC( D) becomes a very ample line bundle which is normally generated. As an application, we characterize some smooth projective surfaces. 

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