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NOTES ON VANISHING CYCLES AND APPLICATIONS
Journal of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2020-10-29 , DOI: 10.1017/s1446788720000403
LAURENŢIU G. MAXIM

Vanishing cycles, introduced over half a century ago, are a fundamental tool for studying the topology of complex hypersurface singularity germs, as well as the change in topology of a degenerating family of projective manifolds. More recently, vanishing cycles have found deep applications in enumerative geometry, representation theory, applied algebraic geometry, birational geometry, etc. In this survey, we introduce vanishing cycles from a topological perspective and discuss some of their applications.

中文翻译:

关于消失周期和应用的说明

半个多世纪前引入的消失循环是研究复杂超曲面奇点胚的拓扑结构以及退化的射影流形族拓扑变化的基本工具。最近,消失循环在枚举几何、表示论、应用代数几何、双有理几何等方面得到了深入的应用。在本次调查中,我们从拓扑的角度介绍了消失循环并讨论了它们的一些应用。
更新日期:2020-10-29
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