Title: Ginzburg-Landau equations on Riemann surfaces of higher genus,
Abstract: We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary
genus. In particular: we explicitly construct the (local moduli space of
gauge-equivalent) solutions in a neighbourhood of a constant curvature branch
of solutions; in linearizing the problem, we find a relation with de Rham
cohomology groups of the surface; we classify holomorphic structures on line
bundles arising as solutions to the equations in terms of the degree, the
Abel-Jacobi map, and symmetric products of the surface; we construct explicitly
the automorphy factors and the equivariant connection on the trivial bundle
over the Poincaré upper complex half plane.