  The superfluid transition of a repulsive Bose gas in the presence of a
sinusoidal potential which represents a simple-cubic optical lattice is
investigate using quantum Monte Carlo simulations. At the average filling of
one particle per well the critical temperature has a nonmonotonic dependence on
the interaction strength, with an initial sharp increase and a rapid
suppression at strong interactions in the vicinity of the Mott transition. In
an optical lattice the positive shift of the transition is strongly enhanced
compared to the homogenous gas. By varying the lattice filling we find a
crossover from a regime where the optical lattice has the dominant effect to a
regime where interactions dominate and the presence of the lattice potential
becomes almost irrelevant.
