Algebraic invariants of singularities

奇点的代数不变量

• 批准号: DP170102328
• 负责人: Prof Christian Haesemeyer
• 金额: $ 24.14万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-15 至 2022-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170102328
• 关键词: Algebraic; invariants; singularities

This project aims to study the local and global behaviour of singularities that algebraic equations can describe via difficult algebraic invariants constructed from (algebraic) functions on the geometric object. A geometric object has a singularity at a point where its tangent directions do not behave the way they should. Examples include black holes, the vertex of a cone or a road intersection. This project is expected to contribute to fundamental research goals in pure mathematics, and increase the international competitiveness of Australian mathematics research.

该项目旨在研究代数方程式可以通过（代数）在几何对象上构建的难度代数不变式来描述的奇异性的局部和全球行为。几何对象在其切线方向无法表现应有的方式上具有奇异性。例子包括黑洞，圆锥形的顶点或道路交叉路口。预计该项目将促进纯数学的基本研究目标，并提高澳大利亚数学研究的国际竞争力。