费米曲线的渐近性：小磁势
Asymptotics for Fermi curves: small magnetic potential
摘要：
我们考虑电和磁周期场的复费米曲线。这些是C^2中的解析曲线，它们是在研究周期薛定谔算子的本征值问题时得到的。我们在C^2区域中刻画了一类这样的曲线，其中至少有一个坐标具有“大”虚部。本文的新结果将以前在无磁场条件下的结果推广到“小”磁场条件下。我们的定理可以用来证明这些费米曲线一般地属于一类无限亏格的黎曼曲面。
英文摘要：
We consider complex Fermi curves of electric and magnetic periodic fields. These are analytic curves in C^2 that arise from the study of the eigenvalue problem for periodic Schroedinger operators. We characterize a certain class of these curves in the region of C^2 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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