Parametrizing Morphisms

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


We continue in this chapter our exposition of background results with a much more specific purpose. We will concentrate on basically one object, whose construction dates back to Grothendieck in 1962: the space parametrizing curves on a given variety, or more precisely morphisms from a given smooth projective curve C to a given smooth quasi-projective variety. Mori’s techniques, which will be discussed in the next chapter, make systematic use of these spaces in a rather exotic way.


Exact Sequence Projective Space Tangent Space Irreducible Component Smooth Projective Curve 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

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

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