Birational equivalences of vortex moduli

S. Bradlow, G. Daskalopoulos, and R. Wentworth

We construct a finite dimensional Kaehler manifold with a holomorphic symplectic circle action whose symplectic reduced spaces may be identified with the tau-vortex moduli spaces (or stable pairs). The Morse theory of the circle action induces natural birational maps between the reduced spaces for different values of tau which in the case of rank two bundles can be canonically resolved in a sequence of blow-ups and blow-downs.