  We study the phase structure of the abelian Higgs model in three dimensions
based on perturbation theory and a set of gauge independent gap equations for
Higgs boson and vector boson masses. Contrary to the non-abelian Higgs model,
the vector boson mass vanishes in the symmetric phase. In the Higgs phase the
gap equations yield masses consistent with perturbation theory. The phase
transition is first-order for small values of the scalar self-coupling
$\lambda$, where the employed loop expansion is applicable.
