Symmetries of Algebraic Varieties in Two and Three Dimensions
A Computational Approach
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Product details:
- Edition number 1
- Publisher Chapman and Hall
- Date of Publication 6 August 2026
- ISBN 9781041088202
- Binding Hardback
- No. of pages342 pages
- Size 234x156 mm
- Language English
- Illustrations 6 Illustrations, black & white; 54 Illustrations, color; 6 Line drawings, black & white; 54 Line drawings, color; 5 Tables, black & white; 3 Tables, color 700
Categories
Short description:
The book explores the computation of the symmetries of algebraic varieties in two and three dimensions. Most of the attention goes to planar and spatial curves and surfaces, defined either implicitly or by means of a rational parametrization.Other algebraic objects, like planar vector fields and finite sets of points, are covered.
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Long description:
Symmetries of Algebraic Varieties in Two and Three Dimensions explores the computation of the symmetries of algebraic varieties in two and three dimensions. Most of the attention goes to curves (both planar and spatial) and surfaces, either implicitly defined or defined by means of a rational parametrization. But other algebraic objects, like planar vector fields and finite sets of points, are also covered.
The book is primarily addressed to researchers and post-graduates, but the content is also accessible to advanced undergraduates with a modest background in computer algebra and algebraic geometry. A primer on these topics is also provided.
Key Features:
- Treats problems in constructive (algebraic) geometry from a computer algebra perspective.
- Accessible and self-contained, assuming only a minimal background in advanced mathematics.
- Each chapter contains a list of open problems related to the chapter, providing topics for further research and inviting the reader to work on specific questions.
Table of Contents:
1. Euclidean symmetries 2. Planar algebraic curves (I): implicit case 3. Planar Algebraic Curves (II): rational curves 4. Planar algebraic vector fields 5. Space algebraic curves 6. Algebraic surfaces (I): implicit surfaces 7. Rational surfaces (I): generalities; ruled surfaces 8. Rational surfaces (II): rational canal surfaces 9. Rational surfaces (III): translational and minimal 10. Finite sets of points
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