Singular Points of Plane Curves

Erscheinungsjahr 2004
ISBN: 978-0-521-54774-1
Verlag: Cambridge University Press

Buch, Englisch, Band 63, 382 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 555 g

Reihe: London Mathematical Society Student Texts

Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.

Autoren/Hrsg.

Wall, C. T. C.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Preface; 1. Preliminaries; 2. Puiseux' theorem; 3. Resolutions; 4. Contact of two branches; 5. Topology of the singularity link; 6. The Milnor fibration; 7. Projective curves and their duals; 8. Combinatorics on a resolution tree; 9. Decomposition of the link complement and the Milnor fibre; 10. The monodromy and the Seifert form; 11. Ideals and clusters; References; Index.