Singular Points of Plane Curves
Singular Points of Plane Curves
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平面曲线的奇异点
DOI：
10.5860/choice.43-1004
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发表时间：
2004
影响因子：
1.2
通讯作者：
C. Wall
中科院分区：
文献类型：
--
作者：
C. Wall
即使是最简单的平面曲线奇点，例如曲线与自身相交或形成尖点的位置最好用复数来理解。完整的处理使用了代数、代数几何、复分析和拓扑学的技术，构成了一个有吸引力的数学章节，可以用作任何这些主题或更高维度的奇点理论的介绍。本书是为研究生设计的入门读物，借鉴了作者教授理科硕士课程的经验；此外，通过综合不同的观点，他对这个主题提出了新颖的观点，并得出了一些新的结果。
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.