An example of a stable but fibrewise nonstable bundle on the twistor\n space of a hyperk "ahler manifold

2018/12/31 by Artour Tomberg, Tomberg, Artour
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1812.11860

openalex publication_date 2018/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an explicit example of a stable bundle on the twistor space\n\Tw(M) of a hyperk "ahler manifold M whose restrictions to all the\nfibres of the natural twistor projection \π : \Tw(M) \→\n mathbbCP¹ are nonstable. We also describe the relationship between bundles\non \Tw(M) that do not have subsheaves of strictly lower rank and\nbundles that stably restrict to the fibres of \π, and announce a result\nwhose proof will appear in a forthcoming paper.\n

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