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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

There is no Bogomolov type restriction theorem for strong semistability in positive characteristic


Author: Holger Brenner
Journal: Proc. Amer. Math. Soc. 133 (2005), 1941-1947
MSC (2000): Primary 14J60, 14H60, 13A35
Published electronically: January 31, 2005
MathSciNet review: 2137859
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Abstract: We give an example of a strongly semistable vector bundle of rank two on the projective plane such that there exist smooth curves of arbitrary high degree with the property that the restriction of the bundle to the curve is not strongly semistable anymore. This shows that a Bogomolov type restriction theorem does not hold for strong semistability in positive characteristic.


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Additional Information

Holger Brenner
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom
Email: H.Brenner@sheffield.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07843-3
PII: S 0002-9939(05)07843-3
Received by editor(s): February 10, 2004
Received by editor(s) in revised form: March 20, 2004
Published electronically: January 31, 2005
Communicated by: Michael Stillman
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.