Coupled vortex equations and Moduli: Deformation theoretic Approach and Kaehler Geometry

dc.creatorBiswas, Indranil
dc.creatorSchumacher, Georg
dc.date2008-08-24
dc.date.accessioned2026-07-07T09:58:11Z
dc.date.available2026-07-07T09:58:11Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/0808.3260
dc.identifierhttp://arxiv.org/abs/0808.3260
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167627
dc.subjectAlgebraic Geometry
dc.subject14J60; 32L05
dc.titleCoupled vortex equations and Moduli: Deformation theoretic Approach and Kaehler Geometry
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