Classification of Higher Dimensional Algebraic Varieties

• Main Authors: Hacon, Christopher D. (Author), Kovács, Sándor (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2010.
• Series: Oberwolfach Seminars ; 41
• Subjects: Mathematics.; Algebraic geometry.; Algebraic Geometry.

This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on...

Table of Contents:

• Basics
• Preliminaries
• Singularities
• Recent advances in the minimal model program
• The main result
• Multiplier ideal sheaves
• Finite generation of the restricted algebra
• Log terminal models
• Non-vanishing
• Finiteness of log terminal models
• Compact moduli spaces of canonically polarized varieties
• Moduli problems
• Hilbert schemes
• The construction of the moduli space
• Families and moduli functors
• Singularities of stable varieties
• Subvarieties of moduli spaces.