On Stable Bundles of Ranks 2 and 3 on P^3
Algebraic Geometry
2007-05-23 v1
Abstract
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) moduli space. We also analyse the case when B is a power of the hyperplane bundle. The same approach is used to study rank 2 bundles on P^3.
Cite
@article{arxiv.math/0310073,
title = {On Stable Bundles of Ranks 2 and 3 on P^3},
author = {Al Vitter},
journal= {arXiv preprint arXiv:math/0310073},
year = {2007}
}
Comments
35 pages,AMSLaTeX