Vortices and Jacobian varieties

Abstract

We investigate the geometry of the moduli space of N vortices on line bundles over a closed Riemann surface σ of genus g>1, in the little explored situation where 1≤N 1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel-Jacobi map of σ at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics. © 2011 Elsevier B.V.