Ruled Varieties

An Introduction to Algebraic Differential Geometry

  • Gerd Fischer
  • Jens Piontkowski

Part of the Advanced Lectures in Mathematics book series (ALM)

Table of contents

  1. Front Matter
    Pages I-X
  2. Gerd Fischer, Jens Piontkowski
    Pages 1-11
  3. Gerd Fischer, Jens Piontkowski
    Pages 12-48
  4. Gerd Fischer, Jens Piontkowski
    Pages 49-118
  5. Gerd Fischer, Jens Piontkowski
    Pages 119-136
  6. Back Matter
    Pages 137-142

About this book

Introduction

Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable.

This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties.

Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course.

Keywords

Algebraische Geometrie Differentialgeometrie Gaussian curvature Grassmannians Ruled Varieties Tangent and Secant Varieties algebraic varieties curvature differential geometry

Authors and affiliations

  • Gerd Fischer
    • 1
  • Jens Piontkowski
    • 1
  1. 1.Mathematisches InstitutHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-80217-0
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2001
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-528-03138-1
  • Online ISBN 978-3-322-80217-0
  • Series Print ISSN 0932-7134
  • About this book