Spectral curves for Cauchy-Riemann operators on punctured elliptic   curves
  We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve if one imposes appropriate boundary conditions. Algebraic curves of the type thus obtained appear as irreducible components of spectral curves of minimal tori with planar ends in R^3. It appears that these curves coincide with the spectral curves of certain elliptic KP solitons as studied by Krichever. 
Christoph Bohle, Iskander A. Taimanov
math.DG math.AG