Trends in Singularities
Trends in Singularities
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奇点的趋势
DOI：
10.1007/978-3-0348-8161-6
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Tibar
中科院分区：
文献类型：
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作者：
A. Libgober;M. Tibar
这一卷中的论文集合代表了在理解奇点的几何和拓扑学方面的最新进展。这本书涵盖了当代奇点理论关注的广泛主题。它的想法是在1999年和2000年在里尔大学(USTL)举行的两次奇点研讨会上产生的。由于奇点理论的广泛性，一本书很难完整地描述今天的进步。尽管如此，这些文件集提供了世纪之交该领域的情况的一个很好的快照。有几篇论文涉及奇点理论的整体方面。具有指定奇点的平面曲线的特征分类是代数几何中的首要问题之一。牛顿知道平面三次曲线的分类，克莱因在19世纪末实现了四次曲线的分类。此后，高次曲线的分类问题在许多著作中得到了解决。在Artal，Carmona和Cogolludo的文章中，作者刻画了具有An(n>；15)型奇点和其他奇点的Milnor数的大的(Le.，：18)和的不可约六次曲线。他们发现了这些家庭的许多有趣的特性。特别是，他们发现了所谓扎里斯基配对的新例子，即
The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n> 15) and a large (Le.,:::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, ie