MOS

Abstract

In this talk I will explain how to construct stable sheaves over K3 fibered threefolds using a relative Fourier-Mukai transform, which describes these sheaves in terms of spectral data. This procedure is similar to the spectral cover construction for elliptic fibrations, which I will also review.

On K3 fibered Calabi-Yau threefolds, the Fourier-Mukai transform induces an embedding of the relative Jacobian of line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves to a generic torus fibration over the moduli space of curves of given arithmetic genus on the Calabi-Yau threefold.