Intersection Theory for Non Intersectional Cycles
非相交循环的相交理论
基本信息
- 批准号:0070409
- 负责人:
- 金额:$ 7.27万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2000
- 资助国家:美国
- 起止时间:2000-07-01 至 2005-09-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In this project the investigator studies the intersection of two cycles whose dimensions do not add up to the dimension of the ambient space. In previous studies of intersection theory this is the case that has been ignored, since in general these cycles do not meet (thus we call them non-intersectional cycles). The space of cycles is a big puzzle to us, and this non-intersectional case is a piece that is still missing from the puzzle. So in order to have a complete picture of space of cycles, one should also include non-intersectional cycles. The first case studied by the investigator was the linking case where the dimensions of cycles add up to the number that is one less than the dimension of the ambient space. The fundamental approach is that such an intersection theory should not only include the cycles that meet, but also those that do not meet. To accomplish this the investigator borrows a tool-Archimedean height pairing from Arakelov geometry (or to be precise, the Arithmetic intersection theory developed by Gillet and Soule), which is only defined for pairs of linking cycles that do not meet. In this direction the investigator has made significant progress: (1) He obtained formulas for the leading term of the asymptotics of Archimedean height pairing. (2) Investigating Mazur's incidence structure, he constructed an incidence divisor on the Chow variety. (3) Based on above two results, he gave a proof of Clemens' conjecture: generic quintic three folds admit only finitely many smooth rational curves of each degree. The plan is to further the understanding of this intersection theory that includes general non-intersectional cycles. The project is concentrated in (1) the study of incidence divisors, (2) the relation between the incidence equivalence and the Abel-Jacobi equivalence, (3) the application to a study of the relation between the Chow group and the Chow variety, (4) the application to a construction of Beilinson-Bloch filtration on the Chow group. One of the most fundamental problems in mathematics is the solving of algebraic equations. Once people it was realized that one could not always explicitly write down the solutions of equations, the paradigm changed into the mode of examining different types of questions such as: does a solution exist, if so, how many solutions are there, do the solution sets have additional structure? These are the fundamental questions in algebraic geometry. In order to answer them, mathematicians have developed varied techniques, one of which-intersection theory--studies he intersection of solution sets of two or more systems of equations. In this project, the investigator plans to develop a new method in intersection theory. The significance of this project is to investigate material that is less studied or completely untouched by the current techniques of intersection theory.
在这个项目中,研究人员研究了两个循环的交叉点,它们的维度加起来不等于周围空间的维度。 在以前的交叉理论研究中,这种情况被忽略了,因为一般来说这些循环并不相交(因此我们称之为非交叉循环)。 循环的空间对我们来说是一个大难题,而这个非交叉的例子是这个难题中仍然缺少的一块。 因此,为了对循环空间有一个完整的了解,我们还应该包括非交叉循环。 研究者研究的第一种情况是连接情况,其中循环的维数加起来等于比周围空间的维数小1的数。 基本的方法是,这样的交集理论不仅应该包括满足的循环,而且还应该包括不满足的循环。 为了实现这一点,研究者借用了阿拉克洛夫几何(或者更准确地说,由吉莱和索尔开发的算术相交理论)的工具阿基米德高度配对,它只定义为不相交的链接循环对。 在这个方向上,研究者取得了重大进展:(1)他获得了阿基米德高度配对渐近性的首项公式。 (2)调查马祖尔的发病率结构,他建造了一个发病率因子的周品种。 (3)基于上述两个结果,他给出了Clemens猜想的一个证明:一般五次三重曲线只允许每一次的光滑有理曲线的个数为1/2。 该计划是为了进一步了解这个交叉理论,包括一般的非交叉周期。 本课题主要研究了关联因子的研究,关联等价与Abel-Jacobi等价的关系,关联等价在Chow群与Chow簇关系研究中的应用,关联等价在Chow群上的Beilinson-Bloch滤子构造中的应用。数学中最基本的问题之一是解代数方程。 一旦人们意识到一个人不能总是明确地写下方程的解,范式就转变为检查不同类型问题的模式,例如:是否存在解,如果存在,有多少解,解集是否有额外的结构? 这些是代数几何中的基本问题。 为了回答这些问题,数学家们开发了多种技术,其中之一--交集理论--研究两个或多个方程组解集的交集。 在这个项目中,研究人员计划开发一种新的交叉理论方法。 这个项目的意义是调查材料,是较少研究或完全接触到目前的技术相交理论。
项目成果
期刊论文数量(0)
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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Bin Wang其他文献
A Retrospective Analysis: Development and Validation of a Nomogram Model for Predicating 30-day Mortality in ST-Segment Elevation Myocardial Infarction Patients
回顾性分析:预测 ST 段抬高型心肌梗死患者 30 天死亡率的列线图模型的开发和验证
- DOI:
10.21203/rs.2.24201/v1 - 发表时间:
2020 - 期刊:
- 影响因子:5.8
- 作者:
Bin Wang;Mao;Manzhen Ying;Cheng - 通讯作者:
Cheng
Improving AGC Performance of Coal-Fueled Thermal Generators Using Multi-MW Scale BESS: A Practical Application
使用多兆瓦规模 BESS 提高燃煤火力发电机的 AGC 性能:实际应用
- DOI:
10.1109/tsg.2016.2599579 - 发表时间:
2018-05 - 期刊:
- 影响因子:9.6
- 作者:
Xiaorong Xie;Yonghong Guo;Bin Wang;Yipeng Dong;Liufeng Mou;Fei Xue - 通讯作者:
Fei Xue
Constrained independent component analysis for hyperspectral unmixing
高光谱分解的约束独立分量分析
- DOI:
10.1109/igarss.2010.5648957 - 发表时间:
2010 - 期刊:
- 影响因子:0
- 作者:
W. Xia;Bin Wang;Liming Zhang - 通讯作者:
Liming Zhang
Gamma-irradiation fluctuates the mRNA N6-methyladenosine (m6A) spectrum of bone marrow in hematopoietic injury
伽马射线照射使造血损伤中骨髓 mRNA N6-甲基腺苷 (m6A) 谱发生波动
- DOI:
10.1016/j.envpol.2021.117509 - 发表时间:
2021 - 期刊:
- 影响因子:8.9
- 作者:
Shuqin Zhang;Jiali Dong;Yuan Li;Huiwen Xiao;Yue Shang;Bin Wang;Zhiyuan Chen;Mengran Zhang;Saijun Fan;Ming Cui - 通讯作者:
Ming Cui
Mechanism analysis on controllable methanol quick combustion
可控甲醇快速燃烧机理分析
- DOI:
10.1016/j.apenergy.2017.08.177 - 发表时间:
2017-11 - 期刊:
- 影响因子:11.2
- 作者:
Guopeng Han;Anren Yao;Chunde Yao;Taoyang Wu;Bin Wang;Hongyuan Wei - 通讯作者:
Hongyuan Wei
Bin Wang的其他文献
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{{ truncateString('Bin Wang', 18)}}的其他基金
Collaborative Research: Promoting Lithium Sulfides Redox Cycle via Atomically Dispersed Active Sites for Batteries
合作研究:通过电池的原子分散活性位点促进硫化锂氧化还原循环
- 批准号:
2129982 - 财政年份:2021
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
Diversity of Tropical Intraseasonal Oscillation
热带季节内振荡的多样性
- 批准号:
2025057 - 财政年份:2020
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
Understanding Essential Dynamics and Predictability of Madden-Julian Oscillation (MJO)
了解马登-朱利安振荡 (MJO) 的基本动力学和可预测性
- 批准号:
1540783 - 财政年份:2015
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
Dynamics of the Boreal Summer Intraseasonal Oscillation: Multiscale Interactions
北方夏季季节内振荡的动力学:多尺度相互作用
- 批准号:
1005599 - 财政年份:2010
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
Evolvable wireless laboratory design and implementation for enhancing undergraduate wireless engineering education
增强本科生无线工程教育的可演化无线实验室设计与实施
- 批准号:
0737297 - 财政年份:2008
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
CRI: IAD Instrumentation of a Measurement and Test System for Open Spectrum Wireless Communication and Networking
CRI:用于开放频谱无线通信和网络的测量和测试系统的 IAD 仪器
- 批准号:
0708469 - 财政年份:2007
- 资助金额:
$ 7.27万 - 项目类别:
Continuing Grant
Dynamics and Moist Thermodynamics of the Boreal Summer Intraseasonal Oscillation
北方夏季季节内振荡的动力学和湿润热力学
- 批准号:
0647995 - 财政年份:2007
- 资助金额:
$ 7.27万 - 项目类别:
Continuing Grant
CRI: Instrumentation of a Hierarchical Wireless Sensor Network Test-bed for Research and Education
CRI:用于研究和教育的分层无线传感器网络测试台的仪器
- 批准号:
0454170 - 财政年份:2005
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
Dynamics of the Boreal Summer Intraseasonal Oscillation
北方夏季季节内振荡的动力学
- 批准号:
0329531 - 财政年份:2003
- 资助金额:
$ 7.27万 - 项目类别:
Continuing Grant
Dynamics of the Boreal Summer Intraseasonal Oscillation
北方夏季季节内振荡的动力学
- 批准号:
0073023 - 财政年份:2000
- 资助金额:
$ 7.27万 - 项目类别:
Standard Grant
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