2001/07/31 by Misha Verbitsky
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coherent sheaf #Connection (principal bundle) #Curvature #Geometry #Geometry and complex manifolds #Gravitational singularity #Holomorphic function #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Sheaf #Square-integrable function #Vector bundle #math.AG #math.DG
paper · pdf · doi:10.2478/s11533-011-0016-0
published as Cent. Eur. J. Math., 2011, 9(3), 535-557 · 37 pages, version 11, reference updated, corrected many minor errors and typos found by the referee
arxiv created 2011/01/16 · openalex publication_date 2011/02/14 · arxiv updated 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant curvature which is not necessary L 2-integrable. We show that such sheaves are polystable.