Restricting Semistable Bundles on the Projective Plane to Conics
Abstract
Description
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.
21 pages,AMSLaTeX Exposition improved, important reference added, minor errors corrected
21 pages,AMSLaTeX Exposition improved, important reference added, minor errors corrected