Singular Points of Plane Curves

Introduction to singularity theory based on MSc course taught by author; novel synthesis, with new results not found elsewhere.

C. T. C. Wall (Author)

9780521547741, Cambridge University Press

Paperback, published 15 November 2004

382 pages, 24 b/w illus. 50 exercises
22.9 x 15.3 x 2.1 cm, 0.535 kg

'The text reflects the author's great expertise in the field in a masterly way … His style of writing mathematics is … motivating and highly inspiring. No doubt, this book will quickly become a widely used standard text on singularities of plane curves, and a valuable reference book, too.' Zentralblatt MATH

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.

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.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]