Special Vanishing Theorems

  • Bernard Shiffman
  • Andrew John Sommese
Part of the Progress in Mathematics book series (PM, volume 56)


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.


Exact Sequence Vector Bundle Line Bundle Complete Intersection Short Exact Sequence 
These 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Bernard Shiffman
    • 1
  • Andrew John Sommese
    • 2
  1. 1.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA

Personalised recommendations