Vector bundles on non-Kähler principal elliptic bundles over surfaces

Abstract: Let a 3-fold X be a principal elliptic bundle over a compact complex surface and suppose that X does not admit a Kähler metric. I shall present results on the moduli space of relatively semistable vector bundles on X of arbitrary rank. These results are derived by an application of a Fourier-Mukai transform and the study of a spectral cover related to it. The talk is based on a common work with V. Brinzanescu and A. Halanay.