Mathematical Sciences: Gaussian Maps and Topology of SurfaceSingularities

数学科学：高斯图和表面奇点拓扑

• 批准号: 8801855
• 负责人: Jonathan Wahl
• 金额: $ 12.05万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801855&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Gaussian; Maps; Topology

This research is in algebraic geometry, specifically studying invariants and deformations of surface singularities. The principal investigator will study two problems in the topology of links of surface singularities; one involves Casson's invariant of a homology 3-sphere, the other involves a mysterious new invariant arising from the principal investigator's work on Miyaoka's inequality for projective surfaces. He will also study a problem arising from surface singularities, the study of "Gaussian maps" for curves and homogeneous spaces. The subject of this research is the topology of algebraic surfaces and their singularities. Certain numerical invariants are attached to these objects which help in classifying them. The principal investigator will study these invariants.

本研究方向为代数几何，主要研究曲面奇异点的不变量和变形。主要研究者将研究曲面奇点链路拓扑中的两个问题；一个涉及到同调3球的Casson不变量，另一个涉及到一个神秘的新不变量，这个不变量来自于首席研究员对投影曲面的Miyaoka不等式的研究。他还将研究由曲面奇点引起的问题，即曲线和齐次空间的“高斯映射”研究。本研究的主题是代数曲面的拓扑结构及其奇异性。某些数值不变量附在这些对象上，有助于对它们进行分类。首席研究员将研究这些不变量。