  Spectral (Bloch) varieties of multidimensional differential operators on
non-simply connected manifolds are defined. In their terms it is given a
description of the analytical dependence of the spectra of magnetic Laplacians
on non-simply connected manifolds on the values of the Aharonov-Bohm fluxes and
a construction of analogues of spectral curves for two-dimensional Dirac
operators on Riemann surfaces and, thereby, new conformal invariants of
immersions of surfaces into 3- and 4-dimensional Euclidean spaces.
