Résume | We introduce the concept of Bergman bundle attached to a hermitian manifold X, assuming the manifold X to be compact, although the results are local for a large part. The Bergman bundle is some sort of infinite dimensional very ample Hilbert bundle whose bers are isomorphic to the standard L2 Hardy space on the complex unit ball; however the bundle is locally trivial only in the real analytic category, and its complex structure is strongly twisted. We compute the Chern curvature of the Bergman bundle, and show that it is strictly positive. Several potential applications to open problems in analytic geometry will be discussed. |