Restricting Semistable Bundles on the Projective Plane to Conics

Details Restricting Semistable Bundles on the Projective Plane to Conics Restricting Semistable Bundles on the Projective Plane to Conics

2003-10-06

arxiv.org/abs/math/0310076v2

Mathematics

Algebraic Geometry

21 pages,AMSLaTeX Exposition improved, important reference added, minor errors corrected

Scientific paper

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.

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