On two-dimensional finite-gap potential Schrodinger and Dirac operators   with singular spectral curves
  We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as the spectral curves of tori immersed into the three-space. 
I.A. Taimanov