Reducible varieties and valuated matroids

可约簇和估值拟阵

• 批准号: 2601878
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2601878
• 关键词: Reducible; varieties; valuated; matroids

A projective algebraic set X in the projective n-space is irreducible if there does not exist a decomposition of X as a union of two strictly smaller projective algebraic sets. In practice, it is not usually easy to determine whether a projective algebraic set is irreducible or not. The aim of this project is to prove the conjecture which aims to say that the information of a projective algebraic set being reducible is always found in the valuated matroid of some degree d corresponding to the degree-d part of the ideal defining our projective algebraic set. We have an explicit result of this conjecture for four different families of projective algebraic sets, and the next step is to check to see if we can work out a proof in more generality. As this is a project in mathematics, it falls under the remit of the Engineering and Physical Sciences Research Council, and there are no official external partners for this project.

如果射影n-空间中的射影代数集X不存在作为两个严格较小的射影代数集的并的分解，则X是不可约的。在实践中，确定一个射影代数集是否不可约通常并不容易。本课题的目的是证明一个猜想，即一个射影代数集的可约信息总是在定义我们的射影代数集的理想的d次部分所对应的d次赋值拟阵中找到的。对于四种不同的射影代数集族，我们已经得到了这个猜想的一个明确的结果，下一步是检查我们是否可以得到更一般的证明。由于这是一个数学项目，属于工程和物理科学研究理事会的职权范围，该项目没有官方的外部合作伙伴。