On the curvature of vortex moduli spaces

Abstract

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric powers of the surface), we prove that, for genus g>1, the holomorphic bisectional curvature of the vortex metrics cannot always be nonnegative in the multivortex case, and this property extends to all Kaehler metrics on certain symmetric powers. Our result rules out an established and natural conjecture on the geometry of the moduli spaces.

arXiv comment25 pages; final version, to appear in Math. Z

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Cited by in corpus (10)

• Vortices and Jacobian varieties
• Quantitative Heegaard Floer cohomology and the Calabi invariant
• Vortices and the Abel-Jacobi map
• Pairs of pants, Pochhammer curves and $L^2$-invariants
• LS-category and sequential topological complexity of symmetric products
• On the curvature of symmetric products of a compact Riemann surface
• Quot schemes and Ricci semipositivity
• On Kaehler structures over symmetric products of a Riemann surface
• The Berry connection of the Ginzburg-Landau vortices
• Configuration Graph Cohomology