  We study abelian gauge-Higgs models on the lattice and consider gauge groups
Z(3) and U(1). For both cases the partition sums are mapped exactly to a dual
representation where the degrees of freedom are surfaces for the gauge fields
and loops of flux that may serve as boundaries for the surfaces represent the
matter fields. Also at finite chemical potential the dual partition sums have
only real and positive contributions and the complex action problem of the
conventional representation is overcome in the dual approach. We apply a local
Metropolis update for the dual degrees of freedom, as well as a generalization
of the worm algorithm to bounded surfaces. Results that illustrate condensation
phenomena as a function of chemical potential are discussed.
