Singular Points of Plane Curves

TRAMA

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

NOTE EDITORE

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.

SOMMARIO

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.

PREFAZIONE

The study of singularities uses techniques from algebra, algebraic geometry, complex analysis and topology. This book introduces graduate students to this attractive area of mathematics. It is based on a MSc course taught by the author and also is an original synthesis, with new views and results not found elsewhere.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780521839044
• Collana: London Mathematical Society Student Texts
• Dimensioni: 229 x 25 x 152 mm Ø 730 gr
• Formato: Copertina rigida
• Illustration Notes: 24 b/w illus. 50 exercises
• Pagine Arabe: 384