Higher-Dimensional Algebraic Geometry

  • Olivier Debarre

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Olivier Debarre
    Pages 1-36
  3. Olivier Debarre
    Pages 37-54
  4. Olivier Debarre
    Pages 55-84
  5. Olivier Debarre
    Pages 85-110
  6. Olivier Debarre
    Pages 111-141
  7. Olivier Debarre
    Pages 143-166
  8. Olivier Debarre
    Pages 167-220
  9. Back Matter
    Pages 221-234

About this book


Higher-Dimensional Algebraic Geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author's goal is to provide an easily accessible introduction to the subject.
The book covers in the beginning preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Mori's minimal model program of classification of algebraic varieties by proving the cone and contraction theorems.
The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction to graduate students and researchers.


Dimension Divisor Grad algebra algebraic geometry algebraic varieties

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2917-4
  • Online ISBN 978-1-4757-5406-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking