Fibrés vectoriels stables avec $\chi=0$ sur une surface abélienne simple

Abstract.

The aim of this work is to establish a birational description of some components of the moduli space of rank two stable vector bundles with $\chi = 0$ over a simple abelian surface.

We describe these bundles as extensions of rank one torsion free sheaves. Subsequently we apply Mukai's Fourier transform for obtaining the birational description of one component in the moduli space. Also, we make the same thing for some bundles of higher rank, with vanishing first Chern class and $\chi = -2$. Thereafter we establish a description of one component of the moduli space of simple bundles with arbitrary rank and and $\chi = 0$.