Classification of Higher Dimensional Algebraic Varieties

✍ Scribed by Christopher D. Hacon, Sándor Kovács (auth.)

• Publisher: Birkhäuser Basel
• Year: 2010
• Tongue: English
• Leaves: 221
• Series: Oberwolfach Seminars 41
• Edition: 1
• Category: Library

✦ Synopsis

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 the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type.

The book is aimed at advanced graduate students and researchers in algebraic geometry.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-1
Introduction....Pages 3-16
Preliminaries....Pages 17-25
Singularities....Pages 27-45
Front Matter....Pages 47-47
Introduction....Pages 49-49
The main result....Pages 51-66
Multiplier ideal sheaves....Pages 67-78
Finite generation of the restricted algebra....Pages 79-81
Log terminal models....Pages 83-87
Non-vanishing....Pages 88-97
Finiteness of log terminal models....Pages 99-102
Front Matter....Pages 103-103
Moduli problems....Pages 105-110
Hilbert schemes....Pages 111-115
The construction of the moduli space....Pages 117-131
Families and moduli functors....Pages 133-140
Singularities of stable varieties....Pages 141-147
Subvarieties of moduli spaces....Pages 149-169
Back Matter....Pages 171-201

✦ Subjects

Algebraic Geometry