Curves and Divisors on Algebraic Varieties

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


In this preliminary chapter (as well as in the next), we gather standard material that will be used throughout the book. That is to say, material that dates mostly from pre-Mori times.


Irreducible Component Algebraic Variety Projective Variety Exceptional Divisor Rational Curf 
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  1. 1.
    Actually, this is not quite true: when we consider moduli spaces of morphisms from a curve to a variety (see Section 2.2), or Hilbert schemes (see 5.6), we will still call them “schemes” although they are only locally Noetherian (they have countably many Noetherian connected components). To stress the point, I will call them “locally Noetherian schemes” whenever possible. These will be the only conflicts with this convention.Google Scholar

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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