Some Properties of Differentiable Varieties and Transformations

1. Front Matter

   Pages I-IX

   PDF

2. Differential Invariants of Point and Dual Transformations

   • Beniamino Segre

   Pages 1-14

3. Local Properties of Analytic Transformations at their United Points

   • Beniamino Segre

   Pages 14-35

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

   • Beniamino Segre

   Pages 35-53

5. Principal and Projective Curves of a Surface, and Some Applications

   • Beniamino Segre

   Pages 53-69

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

   • Beniamino Segre

   Pages 69-87

7. Extensions to Algebraic Varieties

   • Beniamino Segre

   Pages 88-107

8. Veronese Varieties and Modules of Algebraic Forms

   • Beniamino Segre

   Pages 108-132

9. Linear Partial Differential Equations

   • Beniamino Segre

   Pages 132-152

10. Projective Differential Geometry of Systems of Linear Partial Differential Equations

    • Beniamino Segre

    Pages 152-164

11. Correspondences between Topological Varieties

    • Beniamino Segre

    Pages 164-183

12. Back Matter

    Pages 184-198

    PDF

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.

• Algebraic Cases
• Analytic Cases
• Calc
• Calculation
• Differenzierbare Mannigfaltigkeit
• Dimension
• algebraic curve
• algebraic geometry
• algebraic varieties
• character
• differential equation
• differential geometry
• form
• function
• geometry

• Istituto Matematico, Università di Roma, Roma, Italy

  Beniamino Segre