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.
@article{bwmeta1.element.doi-10_2478_s11533-011-0016-0,
author = {Misha Verbitsky},
title = {Hyperholomorphic connections on coherent sheaves and stability},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {535-557},
zbl = {1263.53041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0016-0}
}
Misha Verbitsky. Hyperholomorphic connections on coherent sheaves and stability. Open Mathematics, Tome 9 (2011) pp. 535-557. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0016-0/
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