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Some Properties of Differentiable Varieties and Transformations

With Special Reference to the Analytic and Algebraic Cases

  • Book
  • © 1957
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Overview

Authors:
  1. Beniamino Segre
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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 13)

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Table of contents (9 chapters)

  1. Front Matter

    Pages 2-8
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  2. Differential Invariants of Point and Dual Transformations

    • Beniamino Segre
    Pages 1-14
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  3. Local Properties of Analytic Transformations at their United Points

    • Beniamino Segre
    Pages 14-35
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  4. Invariants of Contact and of Osculation. The Concept of Cross-ratio in Differential Geometry

    • Beniamino Segre
    Pages 35-53
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  5. Principal and Projective Curves of a Surface, and Some Applications

    • Beniamino Segre
    Pages 53-69
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  6. Some Differential Properties in the Large of Algebraic Curves, their Intersections, and Self-correspondences

    • Beniamino Segre
    Pages 69-88
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  7. Extensions to Algebraic Varieties

    • Beniamino Segre
    Pages 88-108
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  8. Veronese Varieties and Modules of Algebraic Forms

    • Beniamino Segre
    Pages 108-132
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  9. Linear Partial Differential Equations

    • Beniamino Segre
    Pages 132-152
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  10. Correspondences between Topological Varieties

    • Beniamino Segre
    Pages 152-171
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  11. Back Matter

    Pages 171-183
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Keywords

About this book

The present volume contains, together with numerous additions and extensions, the course of lectures which I gave at Pavia (26 September till 5 October 1955) by invitation of the «Centro Internazionale Mate­ matico Estivo». The treatment has the character of a monograph, and presents various novel features, both in form and in substance; these are indicated in the notes which will be found at the beginning and end of each chapter. Of the nine parts into which the work is divided, the first four are essentially differential in character, the next three deal with algebraic geometry, while the last two are concerned with certain aspects of the theory of differential equations and of correspondences between topo­ logical varieties. A glance at the index will suffice to give a more exact idea of the range and variety of the contents, whose chief characteristic is that of establishing suggestive and sometimes unforeseen relations between apparently diverse subjects (e. g. differential geometry in the small and also in the large, algebraic geometry, function theory, topo­ logy, etc.); prominence is given throughout to the geometrical viewpoint, and tedious calculations are as far as possible avoided.

Bibliographic Information

  • Book Title: Some Properties of Differentiable Varieties and Transformations

  • Book Subtitle: With Special Reference to the Analytic and Algebraic Cases

  • Authors: Beniamino Segre

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-52764-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1957

  • eBook ISBN: 978-3-642-52764-7Published: 06 December 2012

  • Edition Number: 1

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Algebraic Geometry

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