Skip to main content
SpringerLink
Log in
Birkhäuser

Classification of Higher Dimensional Algebraic Varieties

  • Textbook
  • © 2010

Overview

Authors:
  1. Christopher D. Hacon

    1. Department of Mathematics, University of Utah, Salt Lake City, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Sándor Kovács

    1. Department of Mathematics, University of Washington, Seattle, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Introductory text to an advanced topic of active research
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Basics

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction

      Pages 3-16

    3. Preliminaries

      Pages 17-25

    4. Singularities

      Pages 27-45

  3. Recent advances in the minimal model program

    1. Front Matter

      Pages 47-47
      Download chapter PDF

    2. Introduction

      Pages 49-49

    3. The main result

      Pages 51-66

    4. Multiplier ideal sheaves

      Pages 67-78

    5. Finite generation of the restricted algebra

      Pages 79-81

    6. Log terminal models

      Pages 83-87

    7. Non-vanishing

      Pages 88-97

    8. Finiteness of log terminal models

      Pages 99-102

  4. Compact moduli spaces of canonically polarized varieties

    1. Front Matter

      Pages 103-103
      Download chapter PDF

    2. Moduli problems

      Pages 105-110

    3. Hilbert schemes

      Pages 111-115

    4. The construction of the moduli space

      Pages 117-131

    5. Families and moduli functors

      Pages 133-140

    6. Singularities of stable varieties

      Pages 141-147

    7. Subvarieties of moduli spaces

      Pages 149-169
Back to top

Keywords

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.

Reviews

From the reviews:

“The present text presents the proofs of many results surrounding the minimal model program (MMP) for higher-dimensional varieties. … This text treats the subject in the great generality which is required for getting the most recent results. Hence, it is laden with terminology, all necessary for the modern researcher. … As such, the text will be invaluable for those currently living off of survey articles trying to grasp recent advances in higher-dimensional geometry.” (Michael A. van Opstall, Mathematical Reviews, Issue 2011 f)

“The authors give a detailed account of these new results and the theory of compact moduli spaces of canonically polarised varieties. … the book contains a considerable number of exercises as well as a chapter of hints to solve them. … the authors have made quite an effort to write a text that is both an accessible introduction and a useful reference. … I can only recommend it to researchers and advanced graduate students interested in this highly active field of mathematics.” (Andreas Höring, Zentralblatt MATH, Vol. 1204, 2011)

Authors and Affiliations

  • Department of Mathematics, University of Utah, Salt Lake City, USA

    Christopher D. Hacon

  • Department of Mathematics, University of Washington, Seattle, USA

    Sándor Kovács

Bibliographic Information

  • Book Title: Classification of Higher Dimensional Algebraic Varieties

  • Authors: Christopher D. Hacon, Sándor Kovács

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-0346-0290-7

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2010

  • Softcover ISBN: 978-3-0346-0289-1Published: 27 May 2010

  • eBook ISBN: 978-3-0346-0290-7Published: 02 February 2011

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: 220

  • Topics: Algebraic Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation