  We study the phase diagram of ultracold bosons in an optical lattice near a
Feshbach resonance. Depending on the boson density, the strength of the optical
lattice potential and the detuning from resonance, the ground state can be a
Mott insulator, a superfluid phase with both an atomic and a molecular
condensate, or a superfluid phase with only a molecular condensate. Mott
insulator to superfluid transitions can be induced either by decreasing the
strength of the optical lattice potential or by varying the detuning from the
Feshbach resonance. Quite generally, we find that for a commensurate density
the ground-state may undergo several insulator-superfluid or
superfluid-insulator transitions as the magnetic field is varied through the
resonance.
