Résume | By a theorem of Kodaira, for a line bundle over a compact complex manifold, the positivity of the first Chern class is equivalent to its ampleness. For vector bundles of higher rank, there are several widely used notions of positivity, and the precise relation between them and ampleness is still only conjectural. In this talk we will discuss the relation between positivity of a vector bundle and the positivity of the associated characteristic forms. In particular, we will establish a differential-geometric version Fulton-Lazarfeld theorem on the description of the positive characteristic classes for ample vector bundles. As an interesting byproduct of the proof we will establish a local refinement of the Kempf-Laksov determinantal formula. |