Skip to main content
SpringerLink
Log in
Birkhäuser

Geometry of Higher Dimensional Algebraic Varieties

  • Book
  • © 1997

Overview

Authors:
  1. Yoichi Miyaoka

    1. RIMS, Kyoto University, Kyoto, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Thomas Peternell

    1. Mathematisches Institut der Universität Bayreuth, Bayreuth, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Oberwolfach Seminars (OWS, volume 26)

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 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
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 (7 chapters)

  1. Front Matter

    Pages i-vi
    Download chapter PDF

  2. Geometry of Rational Curves on Varieties

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction: Why Rational Curves?

      • Yoichi Miyaoka, Thomas Peternell
      Pages 3-5

    3. Deformations and Rational Curves

      • Yoichi Miyaoka, Thomas Peternell
      Pages 6-27

    4. Construction of Non-Trivial Deformations via Frobenius

      • Yoichi Miyaoka, Thomas Peternell
      Pages 28-51

    5. Foliations and Purely Inseparable Coverings

      • Yoichi Miyaoka, Thomas Peternell
      Pages 52-74

    6. Abundance for Minimal 3-Folds

      • Yoichi Miyaoka, Thomas Peternell
      Pages 75-96

    7. Rationally Connected Fibrations and Applications

      • Yoichi Miyaoka, Thomas Peternell
      Pages 97-120

  3. Back Matter

    Pages 121-127
    Download chapter PDF

  4. An Introduction to the Classification of Higherdimensional Complex Varieties

    1. Front Matter

      Pages 129-132
      Download chapter PDF

    2. Prerequisites

      • Yoichi Miyaoka, Thomas Peternell
      Pages 133-205

  5. Back Matter

    Pages 206-213
    Download chapter PDF

  6. Back Matter

    Pages 215-218
    Download chapter PDF
Back to top

Keywords

About this book

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub­ ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex­ plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin­ stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Reviews

"Contains nice historical notes and exercises... Many examples are given to illustrate the theory... Beautifully written [with] up-to-date references to the subjects... Highly recommended."

--ZAA

Authors and Affiliations

  • RIMS, Kyoto University, Kyoto, Japan

    Yoichi Miyaoka

  • Mathematisches Institut der Universität Bayreuth, Bayreuth, Germany

    Thomas Peternell

Bibliographic Information

  • Book Title: Geometry of Higher Dimensional Algebraic Varieties

  • Authors: Yoichi Miyaoka, Thomas Peternell

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-0348-8893-6

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1997

  • Softcover ISBN: 978-3-7643-5490-9Published: 20 March 1997

  • eBook ISBN: 978-3-0348-8893-6Published: 06 December 2012

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: VI, 218

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Algebraic Geometry, Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation