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Restricting semistable bundles on the projective plane to conics

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Abstract.

We study the restrictions of rank 2 semistable vector bundles E on to conics. A Grauert-Mülich type theorem on the generic splitting is proven. The jumping conics are shown to have the scheme structure of a hypersurface 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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Authors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, La, 70118, USA

    Al Vitter

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  1. Al Vitter
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Correspondence to Al Vitter.

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Mathematics Subject Classification (2000):Primary:14J60; Secondary:14F05

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Vitter, A. Restricting semistable bundles on the projective plane to conics. manuscripta math. 114, 361–383 (2004). https://doi.org/10.1007/s00229-004-0464-y

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  • DOI: https://doi.org/10.1007/s00229-004-0464-y

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