  We have performed a systematic study of the phase transition in the pure
compact U(1) lattice gauge theory in the extended coupling parameter space
(\beta, \gamma) on toroidal and spherical lattices. The observation of a
non-zero latent heat in both topologies for all investigated \gamma in the
interval [+0.2,-0.4], together with an effective exponent \nu = 1/d when large
enough lattices are considered, lead us to conclude that the phase transition
is first order. For negative \gamma, our results point to an increasingly weak
first order transition as \gamma is made more negative.
