Cohomological Methods

  • Olivier Debarre
Part of the Universitext book series (UTX)


We begin this chapter with a discussion of various models that can be attached to a projective variety and explore in much more detail the leads developed in Chapter 1. One idea was to attach to a projective variety X a preferred member X min of its birational equivalence class with good properties, such as K X min nef. It is then minimal in the sense that any bi-rational map from X min to a smooth projective variety is an isomorphism (Proposition 1.45). This is possible only if X is not uniruled and the (explicit) construction of X min is one of the purposes of Mori’s minimal model program.


Projective Variety Exceptional Divisor Effective Divisor Smooth Projective Variety Cartier Divisor 
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 2001

Authors and Affiliations

  • Olivier Debarre
    • 1
  1. 1.IRMA—Université Louis Pasteur—CNRSStrasbourg CédexFrance

Personalised recommendations