Higher-Dimensional Algebraic Geometry
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ISBN-13:
9780387952277
Veröffentl:
2001
Erscheinungsdatum:
26.06.2001
Seiten:
234
Autor:
Olivier Debarre
Gewicht:
463 g
Format:
243x162x17 mm
Sprache:
Englisch
Beschreibung:
The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then 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 Moris 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.
"Higher-dimensional algebraic geometry" studies the classificatoin theory of algebaric varieties. This very ctive 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 is well-organized.
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.
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