Theoremes d'Annulation et Lieux de Degenerescence en Petit Corang

After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on a smooth projective variety. They imply a part of a conjecture by Fulton and Lazarsfeld about the connectivity of some degeneracy loci.

2000 Mathematics Subject Classification: 14F17

Keywords and Phrases: Théorèmes d'annulation, grassmannienne.

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