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This paper is devoted to the study of Schrödinger operators with periodic magnetic field having zero flux through a fundamental cell of the periodic lattice. These operators have the form \(H_k(A, V)= (i\nabla+ A(x)- k)^2+ V(x)\), where \(A(x)= (A_1(x),\dots, A_d(x))\) is the periodic vector potential to the magnetic field, and \(V(x)\) is the periodic potential of some electric field. The operator \(H_k(A,V)\) describes an electron in \(\mathbb{R}^d\) with quasimomentum \(k\) moving under the influence of \(A(x)\) and \(V(x)\). The main result is that, for generic small periodic magnetic fields of mean zero and generic small Fermi energies, the Fermi surface is strictly convex and does not have inversion symmetry about any point. In particular for \(d=2\) the intersection of the Fermi surface and its inversion in any point is generically a finite set of points. The same statements hold if there exist both electric and magnetic fields. This inversion asymmetry suppresses the mechanism, known as the Cooper channel, responsible for the appearance of superconductivity in weakly-coupled short-range many Fermion systems. Also it is shown that the Fermi surface is always a real analytic subvariety of \(\mathbb{R}^d\) and that it depends holomorphically on \((A,v)\).