Higher-Dimensional Algebraic Geometry. Universitext

Seitenzahl:

233

Gewicht:

463 g

Erschienen bei:

Springer Verlag GmbH

Kurzbeschreibung

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. TOC: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.

Beschreibung

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.

Inhaltsverzeichnis

From the 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

Mehr über...

Mehr über:  Mathematics, Algebraische Geometrie, Algebraic Varieties, Algebraic Geometry, Mathematics / Geometry / Algebraic

Mehr von: 

Mehr von:  Olivier Debarre, Springer Verlag GmbH