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Hyperholomorphic connections on coherent sheaves and stability

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Verbitsky M.

Open Mathematics

2011

tom 9

nr 3

535-557

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.

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1 Open Mathematics

1 Verbitsky M.

1 2011

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Hyperholomorphic connections on coherent sheaves and stability