Abstract
We consider complex Fermi curves of electric and magnetic periodic fields. These are analytic curves in ℂ2 that arise from the study of the eigenvalue problem for periodic Schrödinger operators. We characterize a certain class of these curves in the region of ℂ2 where at least one of the coordinates has "large" imaginary part. The new results in this work extend previous results in the absence of magnetic field to the case of "small" magnetic field. Our theorems can be used to show that generically these Fermi curves belong to a class of Riemann surfaces of infinite genus.
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