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Higher-Dimensional Algebraic Geometry

Author: Olivier Debarre
Publisher: New York, NY : Springer New York, 2001.
Series: Universitext.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Olivier Debarre
ISBN: 9781475754063 147575406X
OCLC Number: 851753981
Description: 1 online resource (xiii, 234 pages).
Contents: Rational Curves and algebraic varieties --
Parametrizing morphisms --
"Bend-and-break" lemmas --
Uniruled and rationally connected varieties --
The rational quotient --
The cone of curves in the smooth case --
Cohomological methods.
Series Title: Universitext.
Responsibility: by Olivier Debarre.

Abstract:

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.

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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 Read more...

 
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