Restricting Semistable Bundles on the Projective Plane to Conics
Abstract
We study the restrictions of rank 2 semistable vector bundles E on P2 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 J2 in P5 of degree c2(E) when c1(E)=0 and of degree c2(E)-1 when c1(E)=-1. Some examples of jumping conics and jumping lines are studied in detail.
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