On the L^2-metric of vortex moduli spaces

Understand

We derive general expressions for the Kaehler form of the L^2-metric in terms of standard 2-forms on vortex moduli spaces.

• In the case of abelian vortices in gauged linear sigma-models, this allows us to compute explicitly the Kaehler class of the L^2-metric.
• As an application we compute the total volume of the moduli space of abelian semi-local vortices.
• In the strong coupling limit, this then leads to conjectural formulae for the volume of the space of holomorphic maps from a compact Riemann surface to projective space.