Debarre Higher-Dimensional Algebraic Geometry

2001
ISBN: 978-1-4757-5406-3
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 234 Seiten, eBook

Reihe: Universitext

Higher-Dimensional AlgebraicGeometry 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Debarre, Olivier

Inhaltsverzeichnis

1 Curves and Divisors on Algebraic Varieties.- 2 Parametrizing Morphisms.- 3 “Bend-and-Break” Lemmas.- 4 Uniruled and Rationally Connected Varieties.- 5 The Rational Quotient.- 6 The Cone of Curves in the Smooth Case.- 7 Cohomological Methods.- References.