Classification of Higher Dimensional Algebraic Varieties

  • Christopher D. Hacon
  • Sándor Kovács

Part of the Oberwolfach Seminars book series (OWS, volume 41)

Table of contents

  1. Front Matter
    Pages i-x
  2. Basics

    1. Front Matter
      Pages 1-1
    2. Pages 3-16
    3. Pages 17-25
    4. Pages 27-45
  3. Recent advances in the minimal model program

    1. Front Matter
      Pages 47-47
    2. Pages 49-49
    3. Pages 51-66
    4. Pages 83-87
    5. Pages 88-97
  4. Compact moduli spaces of canonically polarized varieties

    1. Front Matter
      Pages 103-103
    2. Pages 105-110
    3. Pages 111-115
  5. Back Matter
    Pages 171-201

About this book


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.


Dimension Divisor Grad algebraic geometry algebraic varieties minimal model moduli space projective variety

Authors and affiliations

  • Christopher D. Hacon
    • 1
  • Sándor Kovács
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA

Bibliographic information