  It is shown that modular invariance provides a natural explanation for the
absence of monopoles when assumed to be a discrete gauge symmetry. It follows
that monopoles can not be seen because it is always possible to find a suitable
gauge-fixing in which they are not present. This result relies upon an easy to
prove but non-trivial property of the modular group. A modular-invariant
formulation for the hamiltonian of the electromagnetism is given. No monopole
arises if independent modular transformations are allowed at each point in
space-time where point-like charges are present.
