Biswas, Indranil ; Schumacher, Georg (2009) Coupled vortex equations and moduli: deformation theoretic approach and Kahler geometry Mathematische Annalen, 343 (4). pp. 825-851. ISSN 0025-5831
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Official URL: http://www.springerlink.com/content/nn5l0770742538...
Related URL: http://dx.doi.org/10.1007/s00208-008-0292-6
Abstract
We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kahler manifold X. These solutions are known to be related to polystable triples via a Kobayashi-Hitchin type correspondence. Using a characterization of infinitesimal deformations in terms of the cohomology of a certain elliptic double complex, we construct a Hermitian structure on these moduli spaces. This Hermitian structure is proved to be Kahler. The proof involves establishing a fiber integral formula for the Hermitian form. We compute the curvature tensor of this Kahler form. When X is a Riemann surface, the holomorphic bisectional curvature turns out to be semi-positive. It is shown that in the case where X is a smooth complex projective variety, the Kahler form is the Chern form of a Quillen metric on a certain determinant line bundle.
Item Type: | Article |
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Source: | Copyright of this article belongs to Springer-Verlag. |
ID Code: | 3539 |
Deposited On: | 12 Oct 2010 04:18 |
Last Modified: | 12 Oct 2010 04:18 |
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