Corpus ID: 14506009

On Stable Bundles of Ranks 2 and 3 on P^3

  title={On Stable Bundles of Ranks 2 and 3 on P^3},
  author={A. Vitter},
  journal={arXiv: Algebraic Geometry},
  • A. Vitter
  • Published 6 October 2003
  • Mathematics
  • arXiv: Algebraic Geometry
We study rank 3 stable bundles E on P^3 as extensions of a line bundle B on a smooth surface S in P^3 by the direct sum of three copies of O_{P^3}(-\nu). In most cases, S (the dependency locus of three sections of E(\nu)) lies in the Noether-Lefschetz locus. We give a detailed analysis when S contains a line L and B is constructed from divisors of the form aL+bC for H=L+C a hyperplane section of S. We study the parameter space of this construction and compare it to the full (Gieseker-Maruyama… Expand
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