• Corpus ID: 118084637

Explicit presentations of nonspecial line bundles and secant spaces

  title={Explicit presentations of nonspecial line bundles and secant spaces},
  author={Seonja Kim},
  journal={arXiv: Algebraic Geometry},
  • Seonja Kim
  • Published 1 May 2012
  • Mathematics
  • arXiv: Algebraic Geometry
A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, we define a minimal presentation of L which is minimal with respect to the degree of E among the presentations. If L=K_X -D +E with degE>2 is a minimal, then L is very ample and any q-points of X with q <degE are embedded in general position but the points of E are not. We investigate sufficient… 


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