  We consider a compact Riemann surface with a holomorphic involution, two
marked fixed points of the involution and a divisor obeying an equation up to
linear equivalence of divisors involving all this data. Examples of such data
are Fermi curves of 2-dimensional periodic Schr\"odinger operators. We show
that the equation has a solution if and only if the two marked points are the
only fixed points of the involution.
