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Universitext

Higher-Dimensional Algebraic Geometry

Authors: Debarre, Olivier

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  • ISBN 978-1-4757-5406-3
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Hardcover $74.95
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  • ISBN 978-0-387-95227-7
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Softcover $74.95
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  • ISBN 978-1-4419-2917-4
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  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

From the reviews:

"This is an introductory text based on a course the author gave at Harvard University addressing the … Mori theory. There are essentially two other texts that a student of the subject can consult on this topic. … The first is a very informal introduction to the theory, while the second is very rigorous, covering the widest range of topics. The book under review lies between these two extremes, balancing rigorous detail with plenty of well-illustrated examples." (Mark Gross, Mathematical Reviews, Issue 2002 g)

"The book is based on a course that the author taught at Harvard University. Concentrating on rational curves was a good idea, since their theory is not treated to the same extent in other introductory books … . The text is well-written and user-friendly, and contains lots of examples; it is a further good feature that there are exercises at the end of each chapter. … The book provides a good introduction to higher-dimensional algebraic geometry for graduate students and other interested mathematicians." (Gabor Megyesi, Bulletin of the London Mathematical Society, Issue 35, 2003)

"The book studies the classification theory of algebraic varieties. … The author’s goal is to provide an easily accessible introduction to the subject. The book begins with 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 of classification of algebraic varieties by proving the cone and contraction theorems." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)

"The author’s textbook is based on notes from a class taught at Harvard University. … He has … selected suitable parts of the theory and tried to give basic definitions, essential proofs, and important examples with as many details as possible. … the book provides an excellent source for graduate students … . The exposition of the material is characterized by a very lucid, refined, and user-friendly style of writing. … this book fills a gap in the existing textbook literature on algebraic geometry." (Werner Kleinert, Zentralblatt MATH, Vol. 978, 2002)


Table of contents (7 chapters)

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-1-4757-5406-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-387-95227-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4419-2917-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Higher-Dimensional Algebraic Geometry
Authors
Series Title
Universitext
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-5406-3
DOI
10.1007/978-1-4757-5406-3
Hardcover ISBN
978-0-387-95227-7
Softcover ISBN
978-1-4419-2917-4
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIII, 234
Number of Illustrations and Tables
11 b/w illustrations
Topics