Symmetries of Algebraic Varieties in Two and Three Dimensions

A Computational Approach
1. Auflage 2026
ISBN: 978-1-041-08820-2
Verlag: Taylor & Francis Ltd

Buch, Englisch, 342 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 790 g

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.

Zielgruppe

Academic, Postgraduate, and Undergraduate Advanced

Autoren/Hrsg.

Alcázar, Juan Gerardo

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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

Über Autor(innen)

Juan Gerardo Alcázar is Full Professor of Applied Mathematics in the Department of Physics and Mathematics of the Universidad de Alcalá (Alcalá 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.