Singular Points of Plane Curves

C. T. C. Wall (University of Liverpool), J. Bruce

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English

Cambridge University Press
18 November 2004

Real analysis, real variables; Analytic geometry

Series: 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.

By: C. T. C. Wall (University of Liverpool)
Series edited by: J. Bruce
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 63
Dimensions: Height: 236mm, Width: 159mm, Spine: 26mm
Weight: 655g
ISBN: 9780521839044
ISBN 10: 0521839041
Series: London Mathematical Society Student Texts
Pages: 384
Publication Date: 18 November 2004
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Singular Points of Plane Curves

'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