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Théorèmes d’annulation générique pour les fibrés vectoriels semi-négatifs. (Generic vanishing theorems for semi-negative vector bundles). (French) Zbl 0939.32020
The author generalizes Green-Lazarsfeld’s theorem about generic vanishing for cohomology groups of flat vector bundles to the case of semi-negative vector bundles over compact Kähler manifolds. He also describes the structure of the exceptional sets. These are done by a study of harmonic forms with values in a semi-negative vector bundle.

MSC:
32L20 Vanishing theorems
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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