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Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

Some Properties of Differentiable Varieties and Transformations

With Special Reference to the Analytic and Algebraic Cases

Authors: Segre, Beniamino

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About this book

The present volume contains, together with numerous addition 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 view­ point, and tedious calculations are as far as possible avoided. The exposition has been planned so that it can be followed without much difficulty even by readers who have no special knowledge of the subjects treated.

Table of contents (10 chapters)

  • Differential Invariants of Point and Dual Transformations

    Segre, Prof. Beniamino

    Pages 1-14

  • Local Properties of Analytic Transformations at their United Points

    Segre, Prof. Beniamino

    Pages 14-35

  • Invariants of Contact and of Osculation The Concept of Cross-ratio in Differential Geometry

    Segre, Prof. Beniamino

    Pages 35-53

  • Principal and Projective Curves of a Surface, and Some Applications

    Segre, Prof. Beniamino

    Pages 53-69

  • Some Differential Properties in the Large of Algebraic Curves, their Intersections, and Self-correspondences

    Segre, Prof. Beniamino

    Pages 69-87

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-642-65006-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA in USD
  • ISBN 978-3-642-65008-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Some Properties of Differentiable Varieties and Transformations
Book Subtitle
With Special Reference to the Analytic and Algebraic Cases
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
Series Volume
13
Copyright
1971
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-65006-2
DOI
10.1007/978-3-642-65006-2
Softcover ISBN
978-3-642-65008-6
Edition Number
2
Number of Pages
X, 198
Topics