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

DOI:
https://doi.org/10.1090/S0002-9939-05-07843-3

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:
https://doi.org/10.1090/S0002-9939-05-07843-3

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.