Birational Algebraic Geometry in Characteristic Zero and Positive Characteristic
特征零和正特征的双有理代数几何
基本信息
- 批准号:1801851
- 负责人:
- 金额:$ 50万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-07-01 至 2024-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Algebraic Geometry is one of the oldest and most active areas of mathematics. It plays an important role in many neighboring fields such as Commutative Algebra, Number Theory, Differential Geometry, and String Theory to name a few. Algebraic Geometry studies the solution sets of polynomial equations. These solution sets define geometric objects and it is important to classify them and understand their qualitative behavior. Birational Geometry aims to classify these geometric objects (up to birational isomorphism). This is one of the principal areas of Algebraic Geometry which in recent years has been at the center of spectacular progress. Many important central questions remain. The PI hopes to capitalize on these recent successes to make progress towards the remaining key open problems and conjectures.The principal investigator will conduct research in Algebraic Geometry and especially in Higher Dimensional Birational Algebraic Geometry over algebraically closed fields of characteristic 0 and characteristic p 0. In particular this project is focused on questions related to the minimal model program for threefolds over an algebraically closed field of characteristic p = 2,3,5 including related questions on the inversion of adjunction, and to the minimal model program and the singularities of threefolds over an algebraically closed field of characteristic p 0. The PI also plans to investigate generic vanishing theorems and the birational geometry of varieties defined over an algebraically closed field of characteristic p 0 as well as questions related to the birational geometry of generalized log canonical pairs and to the termination of log-flips in dimension greater or equal than 4 (in characteristic 0).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.
代数几何是数学中最古老和最活跃的领域之一。它在交换代数、数论、微分几何和弦理论等许多邻近领域发挥着重要作用。代数几何研究多项式方程的解集。这些解集定义了几何对象,对它们进行分类和理解它们的定性行为是很重要的。双几何旨在对这些几何对象进行分类(直到双几何同构)。这是代数几何的主要领域之一,近年来一直处于惊人进展的中心。许多重要的核心问题依然存在。PI希望利用这些最近的成功,在剩余的关键开放问题和猜想方面取得进展。首席研究员将在特征0和特征p 0的代数闭场上进行代数几何特别是高维双代数几何的研究。本课题主要研究特征为p = 2,3,5的代数闭域上三倍函数的极小模型规划问题,包括附加反演问题,以及特征为p = 0的代数闭域上三倍函数的极小模型规划和奇异性问题。PI还计划研究在特征为p 0的代数闭域上定义的变量的泛型消失定理和双对数几何,以及与广义对数正则对的双对数几何和大于或等于4维(特征0)的对数翻转的终止有关的问题。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(11)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Generic vanishing in characteristic $$p>0$$ and the geometry of theta divisors
特征 $$p>0$$ 中的通用消失和 theta 除数的几何
- DOI:10.1007/s40574-021-00304-6
- 发表时间:2022
- 期刊:
- 影响因子:0
- 作者:Hacon, Christopher D.;Patakfalvi, Zsolt
- 通讯作者:Patakfalvi, Zsolt
The minimal model program for threefolds in characteristic 5
特征 5 中三重的最小模型程序
- DOI:10.1215/00127094-2022-0024
- 发表时间:2022
- 期刊:
- 影响因子:2.5
- 作者:Hacon, Christopher;Witaszek, Jakub
- 通讯作者:Witaszek, Jakub
Boundedness of minimal partial du Val resolutions of canonical surface foliations
规范表面叶状结构的最小部分du Val分辨率的有界性
- DOI:10.1007/s00208-021-02195-6
- 发表时间:2021
- 期刊:
- 影响因子:1.4
- 作者:Chen, Yen-An
- 通讯作者:Chen, Yen-An
On the connectedness principle and dual complexes for generalized pairs
- DOI:10.1017/fms.2023.25
- 发表时间:2020-10
- 期刊:
- 影响因子:0
- 作者:Stefano Filipazzi;R. Svaldi
- 通讯作者:Stefano Filipazzi;R. Svaldi
On the relative minimal model program for fourfolds in positive and mixed characteristic
- DOI:10.1017/fmp.2023.6
- 发表时间:2020-09
- 期刊:
- 影响因子:0
- 作者:Christopher D. Hacon;J. Witaszek
- 通讯作者:Christopher D. Hacon;J. Witaszek
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Christopher Hacon其他文献
Japanese Cities and Urbanization IGU-Commission
日本城市和城市化 IGU 委员会
- DOI:
- 发表时间:
2005 - 期刊:
- 影响因子:0
- 作者:
Valery Alexeev;Christopher Hacon;Yujiro Kawamata;佐藤 博樹(中村圭介・連合総合生活開発研究所編);小林 敬一・小澤 敬;Kazuhiko YAGO;Masateru Hino - 通讯作者:
Masateru Hino
Termination of (many) 4-dimensional log flips
终止(多次)4 维日志翻转
- DOI:
- 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
Valery Alexeev;Christopher Hacon;Yujiro Kawamata - 通讯作者:
Yujiro Kawamata
Christopher Hacon的其他文献
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{{ truncateString('Christopher Hacon', 18)}}的其他基金
Geometry of analytic and algebraic varieties
解析几何和代数簇
- 批准号:
2301374 - 财政年份:2023
- 资助金额:
$ 50万 - 项目类别:
Standard 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:
1952522 - 财政年份:2020
- 资助金额:
$ 50万 - 项目类别:
Continuing Grant
Birational geometry of algebraic varieties
代数簇的双有理几何
- 批准号:
1300750 - 财政年份:2013
- 资助金额:
$ 50万 - 项目类别:
Continuing Grant
Birational geometry of higher dimensional varieties
高维簇的双有理几何
- 批准号:
0757897 - 财政年份:2008
- 资助金额:
$ 50万 - 项目类别:
Continuing Grant
Birational geometry of complex projective varieties
复射影簇的双有理几何
- 批准号:
0456363 - 财政年份:2005
- 资助金额:
$ 50万 - 项目类别:
Standard Grant
相似国自然基金
同伦和Hodge理论的方法在Algebraic Cycle中的应用
- 批准号:11171234
- 批准年份:2011
- 资助金额:40.0 万元
- 项目类别:面上项目
相似海外基金
CAREER: Birational Geometry and K-stability of Algebraic Varieties
职业:双有理几何和代数簇的 K 稳定性
- 批准号:
2234736 - 财政年份:2023
- 资助金额:
$ 50万 - 项目类别:
Continuing Grant
CAREER: Birational Geometry and Algebraic Dynamics
职业:双有理几何和代数动力学
- 批准号:
2142966 - 财政年份:2022
- 资助金额:
$ 50万 - 项目类别:
Continuing Grant
Birational Geometry and Algebraic Dynamics
双有理几何和代数动力学
- 批准号:
1912476 - 财政年份:2018
- 资助金额:
$ 50万 - 项目类别:
Standard Grant
Birational Geometry and Algebraic Dynamics
双有理几何和代数动力学
- 批准号:
1700898 - 财政年份:2017
- 资助金额:
$ 50万 - 项目类别:
Standard Grant
Birational geometry for higher-dimensional algebraic varieties
高维代数簇的双有理几何
- 批准号:
16H03925 - 财政年份:2016
- 资助金额:
$ 50万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Birational geometry of higher dimensional algebraic varieties
高维代数簇的双有理几何
- 批准号:
16H02141 - 财政年份:2016
- 资助金额:
$ 50万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Topological methods in Galois theory and birational algebraic geometry
伽罗瓦理论和双有理代数几何中的拓扑方法
- 批准号:
438028-2013 - 财政年份:2015
- 资助金额:
$ 50万 - 项目类别:
Postdoctoral Fellowships
Birational geometry of moduli spaces of algebraic sheaves
代数滑轮模空间的双有理几何
- 批准号:
15K04824 - 财政年份:2015
- 资助金额:
$ 50万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Symplectic Birational Geometry and Almost Complex Algebraic Geometry
辛双有理几何和近复代数几何
- 批准号:
EP/N002601/1 - 财政年份:2015
- 资助金额:
$ 50万 - 项目类别:
Research Grant
Topological methods in Galois theory and birational algebraic geometry
伽罗瓦理论和双有理代数几何中的拓扑方法
- 批准号:
438028-2013 - 财政年份:2014
- 资助金额:
$ 50万 - 项目类别:
Postdoctoral Fellowships