Coupled vortex equations and Moduli: Deformation theoretic Approach and Kaehler Geometry
| dc.creator | Biswas, Indranil | |
| dc.creator | Schumacher, Georg | |
| dc.date | 2008-08-24 | |
| dc.date.accessioned | 2026-07-07T09:58:11Z | |
| dc.date.available | 2026-07-07T09:58:11Z | |
| dc.description | We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kaehler 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 Kaehler. The proof involves establishing a fiber integral formula for the Hermitian form. We compute the curvature tensor of this Kaehler 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 Kaehler form is the Chern form of a Quillen metric on a certain determinant line bundle. | |
| dc.identifier | https://arxiv.org/abs/0808.3260 | |
| dc.identifier | http://arxiv.org/abs/0808.3260 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167627 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J60; 32L05 | |
| dc.title | Coupled vortex equations and Moduli: Deformation theoretic Approach and Kaehler Geometry | |
| dc.type | text |