Singularities of Schubert varieties

舒伯特变体的奇点

• 批准号: 341744-2007
• 负责人: Kuttler, Jochen
• 金额: $ 0.87万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=458554
• 关键词: Singularities; Schubert; varieties

The study of symmetries arises in almost all areas of mathematics, and in particular in geometry. In the mathematical language, symmetries usually are described by means of a group acting on an object. As an elementary example one could consider the group of Euclidean motions on the plane, generated by rotations and translations. One can generalize this picture to study the action of Lie groups or (as in the case of this proposal) algebraic groups on vector spaces (like the plane) or more complicated geometric objects. Symmetry groups arise in numerous natural sciences, be it physics (e.g. quantum or classical mechanics), or chemistry (e.g. the symmetries of crystals), or biology (e.g. the symmetries of protein structures).

对称性的研究几乎出现在数学的所有领域，尤其是在几何学中。在数学语言中，对称性通常是通过作用于对象的群来描述的。作为一个基本的例子，我们可以考虑由旋转和平移产生的平面上的欧几里得运动群。人们可以推广这幅图来研究李群或(如本建议的情况)代数群在向量空间(如平面)或更复杂的几何对象上的作用。对称性群出现在许多自然科学中，无论是物理学(如量子力学或经典力学)、化学(如晶体的对称性)或生物学(如蛋白质结构的对称性)。