2008/08/24 by Indranil Biswas, Biswas, Indranil, Georg Schumacher +1
Mathematics · Physics and Astronomy · #14J60 #32L05 #Advanced Mathematical Physics Problems #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14J60 #msc:32L05
paper · pdf · doi:10.48550/arxiv.0808.3260
arxiv created 2008/08/24 · openalex publication_date 2008/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.