Higher-Dimensional Algebraic Geometry
Seiten
2001
Springer-Verlag New York Inc.
978-0-387-95227-7 (ISBN)
Springer-Verlag New York Inc.
978-0-387-95227-7 (ISBN)
Focuses on the classification theory of algebraic varieties. This title starts with preparatory and standard definitions and results. It also discusses various aspects of the geometry of smooth projective varieties with rational curves, and takes the first steps towards Moris minimal model program of classification of algebraic varieties.
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.
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.
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.
| Reihe/Serie | Universitext |
|---|---|
| Zusatzinfo | 11 Illustrations, black and white; XIII, 234 p. 11 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-387-95227-6 / 0387952276 |
| ISBN-13 | 978-0-387-95227-7 / 9780387952277 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 76,90
Nielsen Methods, Covering Spaces, and Hyperbolic Groups
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 153,90
