Hyperholomorphic connections on coherent sheaves and stability

Misha Verbitsky

Open Mathematics (2011)

  • Volume: 9, Issue: 3, page 535-557
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Misha Verbitsky. "Hyperholomorphic connections on coherent sheaves and stability." Open Mathematics 9.3 (2011): 535-557. <http://eudml.org/doc/268995>.

@article{MishaVerbitsky2011,
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.},
author = {Misha Verbitsky},
journal = {Open Mathematics},
keywords = {Hyperkahler manifold; Coherent sheaf; Stable bundle; Twistor space; hyperkähler manifold; coherent sheaf; stable bundle; twistor space},
language = {eng},
number = {3},
pages = {535-557},
title = {Hyperholomorphic connections on coherent sheaves and stability},
url = {http://eudml.org/doc/268995},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Misha Verbitsky
TI - Hyperholomorphic connections on coherent sheaves and stability
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 535
EP - 557
AB - 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.
LA - eng
KW - Hyperkahler manifold; Coherent sheaf; Stable bundle; Twistor space; hyperkähler manifold; coherent sheaf; stable bundle; twistor space
UR - http://eudml.org/doc/268995
ER -

References

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