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Ruled Varieties

An Introduction to Algebraic Differential Geometry

  • Textbook
  • © 2001

Overview

Authors:
  1. Gerd Fischer

    1. Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

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  2. Jens Piontkowski

    1. Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

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  • Spezielle Flächen für Studium und Forschung

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-X
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  2. Review from Classical Differential and Projective Geometry

    • Gerd Fischer, Jens Piontkowski
    Pages 1-11

  3. Grassmannians

    • Gerd Fischer, Jens Piontkowski
    Pages 12-48

  4. Ruled Varieties

    • Gerd Fischer, Jens Piontkowski
    Pages 49-118

  5. Tangent and Secant Varieties

    • Gerd Fischer, Jens Piontkowski
    Pages 119-136

  6. Back Matter

    Pages 137-142
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

    Gerd Fischer, Jens Piontkowski

About the authors

Prof. Dr. em. Gerd Fischer war viele Jahre Professor für Mathematik an der Universität Düsseldorf. Er ist jetzt Gastprofessor an der Fakultät für Mathematik der TU München. Gerd Fischer ist Autor zahlreicher erfolgreicher Lehrbücher, u.a. der Linearen Algebra (vieweg studium - Grundkurs Mathematik).
Dr. Jens Piontkowski ist Hochschuldozent am Mathematischen Institut der Heinrich-Heine-Universität Düsseldorf.

Bibliographic Information

  • Book Title: Ruled Varieties

  • Book Subtitle: An Introduction to Algebraic Differential Geometry

  • Authors: Gerd Fischer, Jens Piontkowski

  • Series Title: Advanced Lectures in Mathematics

  • DOI: https://doi.org/10.1007/978-3-322-80217-0

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Springer Book Archive

  • Copyright Information: Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 2001

  • Softcover ISBN: 978-3-528-03138-1Published: 29 May 2001

  • eBook ISBN: 978-3-322-80217-0Published: 06 December 2012

  • Series ISSN: 0932-7134

  • Series E-ISSN: 2512-7039

  • Edition Number: 1

  • Number of Pages: X, 142

  • Topics: Algebraic Geometry, Probability Theory and Stochastic Processes, Geometry

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