arXiv subjects
Publications and source records attributed to Al Vitter.
We study the restrictions of rank 2 semistable vector bundles E on P^2 to conics. A Grauert-Mulich type theorem on the generic splitting is proven. The jumping conics are shown to have the scheme structure of a hypersurface J_{2} in P^5 of degree c_{2}(E) when c_{1}(E)=0 and of degree c_{2}(E)-1 when c_{1}(E)=-1. Some examples of jumping conics and jumping lines are studied in detail.
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}(-ν). In most cases, S (the dependency locus of three sections of E(ν)) 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.