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.

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

Type produit : Ouvrage Langue : Anglais   Editeur(s) : Springer Auteur(s) : Olivier Debarre   ISBN13 : 978-0-387-95227-7 EAN13 : 9780387952277 ISBN10 : 0-387-95227-6

Parution : 15/07/2001 Edition : 1ère édition   Nb de pages : 230 pages Format : 16 x 24 Couverture : Relié Poids : 470 g Intérieur : Noir et Blanc