Spectral curves for Cauchy-Riemann operators on punctured elliptic curves

Abstract

We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve under appropriate boundary conditions. The algebraic curves thus obtained arise, for example, as irreducible components of the spectral curves of minimal tori with planar ends in ℝ3. It turns out that these curves coincide with the spectral curves of certain elliptic KP solitons studied by Krichever.