Classification of Higher Dimensional Algebraic Varieties (Paperback)

Christopher D. Hacon

ISBN 10: 3034602898 / ISBN 13: 9783034602891

Published by Birkhauser Verlag AG, Basel, 2010

About this Item

Paperback. This book grew out of the Oberwolfach-SeminarHigherDimensionalAlgebraicGeo- tryorganizedbythetwoauthorsinOctober2008. Theaimoftheseminarwas tointroduce advanced PhD students and young researchers to recent advances and research topics in higher dimensional algebraic geometry. The main emphasis was on the minimal model program and on the theory of moduli spaces. The authors would like to thank the Mathematishes Forshunginstitut Oberwolfach for its hospitality and for making the above mentioned seminar possible, the participants to the seminar for their useful comments, and Alex Kuronya, Max Lieblich, and Karl Schwede for valuable suggestions and conversations. The ?rst named author was partially supported by the National Science Foundation under grant number DMS-0757897 and would like to thank Aleksandra, Stefan, Ana, Sasha, Kristina and Daniela Jovanovic-Haconfor their love and continuos support. The second named author was partially supported by the National Science Foun- tion under grant numbers DMS-0554697 and DMS-0856185, and the Craig McKibben and Sarah Merner Endowed Professorship in Mathematics at the University of Wa- ington.He would also like to thank Timea Tihanyi for her enduring love and support throughout and beyond this project and his other co-authors for their patience and und- standing. Contents I Basics 1 1INTRODUCTION 3 1. A. CLASSIFICATION 3 2PRELIMINARIES 17 2. A. NOTATION 17 2. B. DIVISORS 18 2. C. REFLEXIVE SHEAVES 20 2. D. CYCLIC COVERS 21 2. E. R-DIVISORS IN THE RELATIVE SETTING 22 2. F. FAMILIES AND BASE CHANGE 24 2. G. PARAMETER SPACES AND DEFORMATIONS OF FAMILIES 25 3SINGULARITIES 27 3. A. Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783034602891

Bibliographic Details

• Title: Classification of Higher Dimensional Algebraic Varieties (Paperback)
• Publisher: Birkhauser Verlag AG, Basel
• Publication Date: 2010
• Language: English
• ISBN 10: 3034602898
• ISBN 13: 9783034602891
• Binding: Paperback
• Condition: new

About this title

Synopsis

Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.

From the Back Cover

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.