Abstract
There are two methods of generalizing to vector bundles the concept of positivity and cohomology vanishing theorems for line bundles. One method, which we discuss in Chapter VI, is the differential-geometric approach of Nakano and Griffiths that directly uses the Kodaira-Nakano identity. In this chapter, we discuss the other method, which is based on the concept of ampleness due to Grothendieck, Grauert, and Hartshorne and yields the vanishing theorem of Le Potier.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Shiffman, B., Sommese, A.J. (1985). Vector Bundles: Ampleness. In: Vanishing Theorems on Complex Manifolds. Progress in Mathematics, vol 56. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6680-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-6680-3_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-6682-7
Online ISBN: 978-1-4899-6680-3
eBook Packages: Springer Book Archive