Singular points of plane curves
著者
書誌事項
Singular points of plane curves
（London Mathematical Society student texts, 63）
Cambridge University Press, 2004
- : hbk
- : pbk
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注記
Includes bibliographical references (p. 357-367) and index
内容説明・目次
内容説明
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.
目次
- 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.
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