Combinatorial and computational algebra of toric degenerations of varieties

品种环面退化的组合和计算代数

• 批准号: 1953188
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1953188
• 关键词: Combinatorial; computational; algebra; toric; degenerations

Toric varieties play an important role in algebraic geometry. There are several methods developed in polyhedral and combinatorial geometry to compute the invariants of a toric variety.The student will work on toric varieties which are at the interface of algebra, combinatorics and geometry. Recently there has been a breakthrough in algebraic geometry making a direct connection between the theory of Newton-Okounkov bodies and tropical geometry, and in particular the toric varieties arising in both contexts. The main component of the student's project is to apply algebraic and combinatorial methods to further explore such connections.

复曲面簇在代数几何中起着重要的作用。在多面体和组合几何中，有几种方法可以用来计算复曲面簇的不变量。学生将研究代数，组合学和几何学之间的复曲面簇。最近有一个突破，代数几何之间的直接联系理论的牛顿Okounkov机构和热带几何，特别是复曲面品种出现在这两个方面。学生项目的主要组成部分是应用代数和组合方法来进一步探索这种联系。

项目成果

Conditional probabilities via line arrangements and point configurations

通过线排列和点配置的条件概率

• DOI: 10.1080/03081087.2021.1912693
• 发表时间: 2021
• 期刊: Linear and Multilinear Algebra
• 影响因子: 1.1
• 作者: Clarke O

Toric degenerations of flag varieties from matching field tableaux

匹配田野场景中旗帜品种的环面退化

• DOI: 10.48550/arxiv.1904.07832
• 发表时间: 2019
• 期刊: arXiv e-prints
• 作者: Clarke Oliver

Conditional independence ideals with hidden variables

具有隐变量的条件独立理想

• DOI: 10.48550/arxiv.1901.03059
• 发表时间: 2019
• 期刊: arXiv e-prints
• 作者: Clarke Oliver

Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux

来自匹配现场场景的格拉斯曼派和舒伯特变体的环面退化

• DOI: 10.48550/arxiv.1904.00981
• 发表时间: 2019
• 期刊: arXiv e-prints
• 作者: Clarke Oliver