FRG: Collaborative Research: Arithmetic and geometry of rational curves on K3 surfaces
FRG:协作研究:K3 曲面上有理曲线的算术和几何
基本信息
- 批准号:0968318
- 负责人:
- 金额:$ 47.05万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2010
- 资助国家:美国
- 起止时间:2010-07-01 至 2014-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project addresses the theory of rational curves on K3 surfaces, as a prototype and model for investigations of rational curves on higher-dimensional varieties of Fano and intermediate type. The key problems concern the existence of infinitely many rational curves on K3 surfaces over countable fields, techniques for the generation of such curves and computation of their numerical invariants, Brill-Noether loci and enumerative geometry of rational curves, aspects of mixed-characteristic deformation theory, Galois representations, and Brauer groups.The term `K3 surface' was coined by A. Weil in the 1950's, and honors the seminal contributions of Kummer, Kaehler, and Kodaira to their structure. These surfaces have been central to complex geometry for decades, but recently their arithmetic properties have received increasing attention. This project addresses problems at the interface of complex, algebraic, and arithmetic geometry. In particular, what is the structure of the curves on a K3 surface? Can they be constructed explicitly? And how do they reflect symmetries of the ambient surface?
该项目致力于K3曲面上的有理曲线理论,作为Fano和中间类型高维品种上有理曲线研究的原型和模型。 其关键问题涉及可数域上K3曲面上无穷多条有理曲线的存在性、这类曲线的生成技术及其数值不变量的计算、有理曲线的Brill-Noether轨迹和计数几何、混合特征形变理论、Galois表示和Brauer群等方面。韦尔在20世纪50年代,并荣誉的开创性贡献的库默,凯勒,和科代拉,他们的结构。 这些曲面几十年来一直是复杂几何的核心,但最近它们的算术性质受到越来越多的关注。 这个项目解决了复杂的,代数的和算术几何的接口问题。 特别是,K3曲面上的曲线结构是什么? 它们可以被显式地构造吗? 它们如何反映周围表面的对称性?
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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Yuri Tschinkel其他文献
Homomorphisms of multiplicative groups of fields preserving algebraic dependence
- DOI:
10.1007/s40879-018-00312-5 - 发表时间:
2019-01-07 - 期刊:
- 影响因子:0.500
- 作者:
Fedor A. Bogomolov;Marat Rovinsky;Yuri Tschinkel - 通讯作者:
Yuri Tschinkel
Reconstruction of Function Fields
- DOI:
10.1007/s00039-008-0665-8 - 发表时间:
2008-06-23 - 期刊:
- 影响因子:2.500
- 作者:
Fedor Bogomolov;Yuri Tschinkel - 通讯作者:
Yuri Tschinkel
Fonctions ZÊta Des Hauteurs Des Espaces Fibrés
纤维空间高级功能
- DOI:
- 发表时间:
2000 - 期刊:
- 影响因子:0
- 作者:
Antoine Chambert;Yuri Tschinkel - 通讯作者:
Yuri Tschinkel
Бирациональные типы алгебраических орбифолдов
Бирациональные типы алгебраических орбифолдов
- DOI:
10.4213/sm9386 - 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Эндрю Креш;Andrew Kresch;Юрий Чинкель;Yuri Tschinkel - 通讯作者:
Yuri Tschinkel
Simple Examples of Symplectic Four-manifolds with Exotic Properties
- DOI:
10.1023/a:1022372407184 - 发表时间:
2003-01-01 - 期刊:
- 影响因子:1.000
- 作者:
Fedor Bogomolov;Yuri Tschinkel - 通讯作者:
Yuri Tschinkel
Yuri Tschinkel的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Yuri Tschinkel', 18)}}的其他基金
Rationality and Stable Rationality of Algebraic Varieties
代数簇的有理性和稳定有理性
- 批准号:
2000099 - 财政年份:2020
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
Birational Geometry and Rational Points
双有理几何和有理点
- 批准号:
1601912 - 财政年份:2016
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
Spaces of rational curves and diophantine geometry
有理曲线空间和丢番图几何
- 批准号:
1160859 - 财政年份:2012
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
Rational Points & Rational Curves on Algebraic Varieties
理性点
- 批准号:
0901777 - 财政年份:2009
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
COLLABORATIVE RESEARCH: EMSW21-RTG: JOINT COLUMBIA-CUNY-NYU RESEARCH TRAINING GROUP IN NUMBER THEORY
合作研究:EMSW21-RTG:哥伦比亚大学-纽约市立大学-纽约大学联合数论研究培训小组
- 批准号:
0739380 - 财政年份:2008
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
Collaborative Research: FRG: Geometry of moduli spaces of rational curves with applications to Diophantine problems over function fields
合作研究:FRG:有理曲线模空间的几何及其在函数域上丢番图问题的应用
- 批准号:
0554280 - 财政年份:2006
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
Arithmetic and Geometry of Algebraic Varieties
代数簇的算术和几何
- 批准号:
0100277 - 财政年份:2001
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
相似海外基金
FRG: Collaborative Research: New birational invariants
FRG:协作研究:新的双有理不变量
- 批准号:
2244978 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245017 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245111 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245077 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2244879 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
FRG: Collaborative Research: New Birational Invariants
FRG:合作研究:新的双理性不变量
- 批准号:
2245171 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2403764 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245021 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245097 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245147 - 财政年份:2023
- 资助金额:
$ 47.05万 - 项目类别:
Continuing Grant