Fourier-Mukai transform and adiabatic curvature of spectral bundles for Landau Hamiltonians on Riemann surfaces

摘要

We study the family of Landau Hamiltonians on a Riemann surface S by means of a Nahm transform and an integral functor related to the Fourier-Mukai transform associated to its jacobian variety J(S). This approach allows us to explicitly determine the spectral bundles (P) over capq --> J(S) associated to the holomorphic Landau levels. As a first main result we prove that these spectral bundles are holomorphic stable bundles with respect to the canonical polarization of J(S) determined by the theta divisor Theta.