Abstract

In this chapter we consider some important special cases. First we prove a comprehensive vanishing theorem for line bundles on projective space. In Chapters V and VI, we use part of this theorem to extend the vanishing theorems of Chapters II and III to vector bundles. We then discuss line bundles on projective hypersurfaces, in particular quadrics, and on complete intersections. Finally, we state a vanishing theorem of Le Potier for Grassmannians.KeywordsExact SequenceVector BundleLine BundleComplete IntersectionShort Exact SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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