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

2004/01/26 by Holger Brenner, Brenner, Holger
Mathematics · #13A35 #14H60 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #advanced mathematical theories #math.AC #math.AG #msc:13A35 #msc:14H60 #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/0401366

arxiv created 2004/01/26 · openalex publication_date 2004/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Vector bundles and p-adic representations I

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