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Geometry of Higher Dimensional Algebraic Varieties

  • Yoichi Miyaoka
  • Thomas Peternell

Part of the DMV Seminar book series (OWS, volume 26)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Geometry of Rational Curves on Varieties

    1. Front Matter
      Pages 1-1
    2. Yoichi Miyaoka, Thomas Peternell
      Pages 3-5
    3. Yoichi Miyaoka, Thomas Peternell
      Pages 6-27
    4. Yoichi Miyaoka, Thomas Peternell
      Pages 28-51
    5. Yoichi Miyaoka, Thomas Peternell
      Pages 52-74
    6. Yoichi Miyaoka, Thomas Peternell
      Pages 75-96
    7. Yoichi Miyaoka, Thomas Peternell
      Pages 97-120
    8. Back Matter
      Pages 121-127
  3. An Introduction to the Classification of Higherdimensional Complex Varieties

    1. Front Matter
      Pages 129-132
    2. Yoichi Miyaoka, Thomas Peternell
      Pages 133-205
    3. Back Matter
      Pages 206-213
  4. Back Matter
    Pages 215-218

About this book

Introduction

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.

Keywords

Algebra Complex analysis Manifold algebraic geometry algebraic varieties calculus complex analyisis geometry proof theorem

Authors and affiliations

  • Yoichi Miyaoka
    • 1
  • Thomas Peternell
    • 2
  1. 1.RIMSKyoto UniversityKyotoJapan
  2. 2.Mathematisches Institut der Universität BayreuthBayreuthGermany

Bibliographic information