Singular Points of Plane Curves
Singular Points of Plane Curves by C. T. C. Wall, published by Cambridge University Press on November 15, 2004, is a comprehensive exploration of the singularities of planar curves. This 370-page book is written in English and delves into the complexities of mathematical concepts, particularly focusing on how even simple singularities, such as self-intersections and cusps, can be understood through the lens of complex numbers. The author employs techniques from algebra, algebraic geometry, complex analysis, and topology to present a cohesive introduction to these topics.
Readers will find that this book serves as an accessible entry point for graduate students interested in singularity theory and its applications in higher dimensions. By synthesizing various perspectives, Wall offers a unique viewpoint on the subject, alongside a number of new results that enhance the understanding of mathematical analysis and geometry. This edition is particularly valuable for those looking to deepen their knowledge in these areas while benefiting from the author’s extensive teaching experience.
Official synopsis Publisher
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.
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