Displaying similar documents to “Hyperholomorphic connections on coherent sheaves and stability”

Stable bundles on hypercomplex surfaces

Ruxandra Moraru, Misha Verbitsky (2010)

Open Mathematics

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A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures...

A note on characterization of Moishezon spaces.

K. Rama (1990)

Publicacions Matemàtiques

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In this note a necessary and sufficient condition for a compact complex space X to be Moishezon is obtained; it can be seen as the existence of a line bundle L on X such that, for some point x ∈ X, the first cohomology groups of X with values respectively in L ⊗ m and L ⊗ m , vanish. (Here m denotes the ideal sheaf at x).

Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space

Indranil Biswas (1997)

Annales de l'institut Fourier

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The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.

Perturbations of the metric in Seiberg-Witten equations

Luca Scala (2011)

Annales de l’institut Fourier

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Let M a compact connected oriented 4-manifold. We study the space Ξ of Spin c -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on M . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all Spin c -structures  Ξ . We prove that, on a complex Kähler surface, for an hermitian metric h sufficiently close to the original Kähler metric, the...