Symmetries of Algebraic Varieties in Two and Three Dimensions
A Computational Approach
1st Edition
Will be published approx. on 6. August 2026
342 pages
978-1-040-58837-6 (ISBN)
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.
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.
More details
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Illustrations
3 Tables, color; 5 Tables, black and white; 54 Line drawings, color; 6 Line drawings, black and white; 54 Illustrations, color; 6 Illustrations, black and white
File size
35,42 MB
ISBN-13
978-1-040-58837-6 (9781040588376)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Juan Gerardo Alcazar
Symmetries of Algebraic Varieties in Two and Three Dimensions
A Computational Approach
Book
approx. 08/2026
1st Edition
CRC Press
€123.50
Not yet published
Person
Juan Gerardo Alcazar is Full Professor of Applied Mathematics in the Department of Physics and Mathematics of the Universidad de Alcala (Alcala de Henares, Madrid, Spain), where he got his Ph.D. in Mathematics in 2007. He has authored and co-authored more than fifty research papers on Computer Algebra and Constructive Algebraic Geometry, most of them related to the interplay between Symbolic Computation and the effective solution of geometric problems on algebraic varieties, mainly curves and surfaces. His most cherished research topics are the effective computation of the topology of algebraic curves and surfaces, offset varieties, detection of special types of curves and surfaces, and efficient checking of symmetries, affine and projective equivalences.
Content
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
