Hyperholomorphic connections on coherent sheaves and stability

• Autorzy: Misha Verbitsky
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hyperkahler manifold; Coherent sheaf; Stable bundle; Twistor space

Kategorie tematyczne

• 53C05: Connections, general theory
• 53C38: Calibrations and calibrated geometries
• 53C26: Hyper-K\"ahler and quaternionic K\"ahler geometry, ``special'' geometry
• 53C55: Hermitian and K\"ahlerian manifolds
• 53C07: Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
• 53C28: Twistor methods
• 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 535-557

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Misha Verbitsky

• SU-HSE

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0016-0