Combinatorics and commutative algebra of algebraic varieties with group actions

具有群作用的代数簇的组合学和交换代数

• 批准号: RGPIN-2017-05732
• 负责人: Rajchgot, Jenna
• 金额: $ 1.53万
• 依托单位: University of Saskatchewan
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635456
• 关键词: Combinatorics; commutative; algebra; algebraic; varieties

Algebraic geometry is a central area of mathematics. It has importance not just in pure and applied mathematics, but also in the natural sciences, engineering, and beyond (eg. economics). At its core, algebraic geometry is the study of common zeros of collections of polynomials in multiple variables. A general theme in the field is to translate geometric questions about these zero-sets, or algebraic varieties, into equivalent algebraic questions. Examples of such geometric questions include "does this zero-set have multiple components?" and "are there any singularities?".

代数几何是数学的一个中心领域。它不仅在纯数学和应用数学中很重要，而且在自然科学、工程等领域也很重要。经济学)。代数几何的核心是研究多变量多项式集合的公共零。该领域的一个普遍主题是将关于这些零集或代数变体的几何问题转化为等价代数问题。这类几何问题的例子包括“这个零集有多个分量吗？”和“有奇点吗？”