The Reconstruction and Recognition Problems for Hypersurface Singularities

超曲面奇点的重建与识别问题

• 批准号: DP140100296
• 负责人: Prof Alexander Isaev
• 金额: $ 26.22万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100296
• 关键词: Reconstruction; Recognition; Problems; Hypersurface; Singularities

This project concerns pure basic research in mathematics. It is centred around a surprising relationship between geometric objects called quasi-homogeneous isolated hypersurface singularities, and algebraic structures described as Artinian Gorenstein algebras. This relationship has not been fully understood despite numerous attempts by internationally based experts to shed light on it. Armed with a novel approach to Artinian Gorenstein algebras, this project proposes to clarify the nature of this relationship and utilise it for solving related geometric and algebraic problems. In particular, it aims at obtaining a groundbreaking result in the area of classical invariant theory.

这个项目涉及纯粹的数学基础研究。它的中心是一个令人惊讶的几何对象之间的关系，称为准齐次孤立超表面奇点，和代数结构描述为阿提尼戈伦斯坦代数。尽管国际专家多次尝试阐明这种关系，但人们仍未完全理解。本项目采用一种新颖的方法来研究artini - Gorenstein代数，旨在阐明这种关系的本质，并利用它来解决相关的几何和代数问题。特别是，它旨在获得经典不变理论领域的突破性成果。