%0 Journal Article %T Spectral curves for Cauchy-Riemann operators on punctured elliptic curves %A Christoph Bohle %A Iskander A. Taimanov %J Mathematics %D 2012 %I arXiv %X 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. %U http://arxiv.org/abs/1212.5147v1