K-Stability in Higher Dimensional Geometry
高维几何中的 K 稳定性
基本信息
- 批准号:2201349
- 负责人:
- 金额:$ 75万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2022
- 资助国家:美国
- 起止时间:2022-09-01 至 2027-08-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The project in algebraic geometry is a study of varieties, which are geometric spaces defined by polynomial equations. Among all geometric spaces, varieties have the advantage of being easier to study from a computational viewpoint. Moreover, since every space can be approximated by varieties, they are crucial construct for algebraic geometers. Inspired by the study of spaces with a metric satisfying certain Einstein field equations, the main aim of the proposal is to provide a new framework to understand varieties which are positively curved, in both global and local settings. One focus will be how these varieties vary in families, and degenerate to others with more special structures. There are several research thrusts to this project. First, the PI aims to solve the local higher rank finite generation conjecture, and thus, complete the local stability theory by establishing the stable degeneration conjecture for any Kawamata log terminal singularity. In addition, the project includes investigation into the moduli theory for general Fano varieties without a K-stability assumption and a study of K-stability for explicit examples of Fano varieties. There are also aims to combine birational and non-archimedean geometry together to understand degenerations of Calabi-Yau manifolds. Graduate students will participate in the research project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
代数几何中的课题是对变量的研究,变量是由多项式方程定义的几何空间。在所有几何空间中,从计算的角度来看,变量具有更容易研究的优点。此外,由于每一个空间都可以被变异近似,它们是代数几何的重要构造。受度量满足某些爱因斯坦场方程的空间研究的启发,该提案的主要目的是提供一个新的框架来理解全局和局部环境下正弯曲的变化。一个重点将是这些品种如何在家庭中变化,并退化到具有更特殊结构的其他品种。这个项目有几个研究重点。首先,PI的目的是解决局部高阶有限生成猜想,从而通过建立任意Kawamata对数端点奇点的稳定退化猜想来完成局部稳定性理论。此外,本项目还研究了不含k稳定性假设的一般Fano品种的模理论,并研究了Fano品种的显式例子的k稳定性。还有一些目标是将两种几何和非阿基米德几何结合在一起,以理解Calabi-Yau流形的退化。研究生将参与研究项目。该奖项反映了美国国家科学基金会的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Chenyang Xu其他文献
Recent Advances in DNA Repair Pathway and Its Application in Personalized Care of Metastatic Castration-Resistant Prostate Cancer (mCRPC).
DNA 修复途径的最新进展及其在转移性去势抵抗性前列腺癌 (mCRPC) 个体化护理中的应用。
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Chenyang Xu;Shanhua Mao;Haowen Jiang - 通讯作者:
Haowen Jiang
K-stability of Fano varieties: an algebro-geometric approach
- DOI:
10.4171/emss/51 - 发表时间:
2020-11 - 期刊:
- 影响因子:2.3
- 作者:
Chenyang Xu - 通讯作者:
Chenyang Xu
Effectiveness of the log Iitaka fibration for 3-folds and 4-folds
3 倍和 4 倍对数 Iitaka 纤维化的有效性
- DOI:
10.2140/ant.2009.3.697 - 发表时间:
2009 - 期刊:
- 影响因子:1.3
- 作者:
Gueorgui Todorov;Chenyang Xu - 通讯作者:
Chenyang Xu
Multi‑index base‑stock policy for inventory systems with multiple capacitated suppliers
具有多个供应商的库存系统的多指数基础库存策略
- DOI:
10.1007/s00291-021-00658-5 - 发表时间:
2021 - 期刊:
- 影响因子:2.7
- 作者:
Chaolin Yang;Diyuan Huang;Chenyang Xu - 通讯作者:
Chenyang Xu
A summary of geometric level-set analogues for a general class of parametric active contour and surface models
一般类参数化活动轮廓和曲面模型的几何水平集类似物总结
- DOI:
10.1109/vlsm.2001.938888 - 发表时间:
2001 - 期刊:
- 影响因子:0
- 作者:
Chenyang Xu;A. Yezzi;Jerry L Prince - 通讯作者:
Jerry L Prince
Chenyang Xu的其他文献
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{{ truncateString('Chenyang Xu', 18)}}的其他基金
FRG: Collaborative Research: Algebraic Geometry and Singularities in Positive and Mixed Characteristic
FRG:合作研究:代数几何和正特征和混合特征中的奇点
- 批准号:
2139613 - 财政年份:2021
- 资助金额:
$ 75万 - 项目类别:
Continuing Grant
K-stability and Higher Dimensional Geometry
K 稳定性和高维几何
- 批准号:
2153115 - 财政年份:2021
- 资助金额:
$ 75万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Algebraic Geometry and Singularities in Positive and Mixed Characteristic
FRG:合作研究:代数几何和正特征和混合特征中的奇点
- 批准号:
1952531 - 财政年份:2020
- 资助金额:
$ 75万 - 项目类别:
Continuing Grant
K-stability and Higher Dimensional Geometry
K 稳定性和高维几何
- 批准号:
1901849 - 财政年份:2019
- 资助金额:
$ 75万 - 项目类别:
Continuing Grant
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