An ampleness criterion for rank 2 vector bundles on surfaces

2018/06/01 by Arnaud Beauville, Beauville, Arnaud · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.1806.00243

openalex publication_date 2018/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We observe that the proof of the Bogomolov stable restriction theorem can be adapted to give an ampleness criterion for globally generated rank 2 vector bundles on certain surfaces. This applies to the Lazarsfeld-Mukai bundles, to congruences of lines in P³, and possibly to the construction of surfaces with ample cotangent bundle (help welcome!).

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• Maximal variation of linear systems

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