Free Resolutions in Commutative Algebra
交换代数中的自由解析
基本信息
- 批准号:1702125
- 负责人:
- 金额:$ 19.2万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-09-01 至 2021-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
A core goal in the mathematical areas Algebraic Geometry and Commutative Algebra deals with understanding the solutions of a system of polynomial equations, possibly in a large number of variables and with a large number of equations. The solutions form a geometric object. The main idea is to study the rich and beautiful interplay between its geometric and algebraic properties. Closely related to this study is the concept of a free resolution, which was first introduced by David Hilbert in two papers in 1890 and 1893. Constructing a free resolution amounts to repeatedly solving systems of polynomial equations. The study of these objects flourished in the second half of the twentieth century, and has seen spectacular progress in the last ten years. The field is very broad, with strong connections and applications to other mathematical areas and string theory. Recent computational methods have made it possible to compute some free resolutions by computers. The main research goal in this project is to make significant progress in understanding the structure of free resolutions and their numerical invariants. The main research topics are:(1) resolutions over complete intersections, which will be studied using the methods recently introduced by Eisenbud and Peeva in their research monograph "Minimal Free Resolutions over Complete Intersections";(2) Betti numbers of periodic infinite minimal free resolutions, for which computational algebra methods will be combined with insights from the examples of modules with periodic resolutions with constant Betti numbers;(3) applications of the new approach introduced recently by McCullough and Peeva which produces resolutions of prime ideals.
在数学领域,代数几何和交换代数的一个核心目标是了解多项式方程组的解,可能是在大量变量和大量方程中。这些解形成了一个几何对象。其主要思想是研究它的几何和代数性质之间丰富而美丽的相互作用。与这项研究密切相关的是自由决议的概念,它是由大卫·希尔伯特在1890年和1893年的两篇论文中首次提出的。构造自由解相当于重复求解多项式方程组。对这些物体的研究在20世纪下半叶蓬勃发展,并在最近十年中取得了令人瞩目的进展。这个领域非常广泛,与其他数学领域和弦理论有着很强的联系和应用。最近的计算方法使用计算机计算一些自由分辨率成为可能。这个项目的主要研究目标是在理解自由分辨率及其数值不变量的结构方面取得重大进展。主要研究内容是:(1)完全交上的分解,将使用Eisenbud和Peeva最近在他们的研究专著《完全交上的最小自由分解》中介绍的方法来研究;(2)周期无限极小自由分解的Betti数,对于它,计算代数方法将与具有常数Betti数的周期分解的例子相结合;(3)McCullough和Peeva最近引入的产生素理想分解的新方法的应用。
项目成果
期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Regularity of prime ideals
素理想的正则性
- DOI:10.1007/s00209-018-2089-y
- 发表时间:2019
- 期刊:
- 影响因子:0.8
- 作者:Caviglia, Giulio;Chardin, Marc;McCullough, Jason;Peeva, Irena;Varbaro, Matteo
- 通讯作者:Varbaro, Matteo
Non-commutative CI operators
非交换 CI 运算符
- DOI:10.1090/proc/14480
- 发表时间:2019
- 期刊:
- 影响因子:1
- 作者:Eisenbud, David;Peeva, Irena;Schreyer, Frank-Olaf
- 通讯作者:Schreyer, Frank-Olaf
Minimal Resolutions Over Codimension 2 Complete Intersections
余维 2 完整交集的最小分辨率
- DOI:10.1007/s40306-018-0293-9
- 发表时间:2019
- 期刊:
- 影响因子:0.5
- 作者:Eisenbud, David;Peeva, Irena
- 通讯作者:Peeva, Irena
{{
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 }}
Irena Peeva其他文献
Koszul graded Möbius algebras and strongly chordal graphs
- DOI:
10.1007/s00029-025-01029-6 - 发表时间:
2025-03-05 - 期刊:
- 影响因子:1.200
- 作者:
Adam LaClair;Matthew Mastroeni;Jason McCullough;Irena Peeva - 通讯作者:
Irena Peeva
Far-Out Syzygies
遥远的 Syzygies
- DOI:
10.1007/978-3-319-26437-0_6 - 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
David Eisenbud;Irena Peeva - 通讯作者:
Irena Peeva
Commutative Algebra, Expository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday
交换代数,在 David Eisenbud 75 岁生日之际献给他的说明性论文
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Iyengar Srikanth B.;Takahashi Ryo;Ryo Takahashi;高橋 亮;高橋 亮;飯間 圭一郎; 松井 紘樹; 嶋田 芳; 高橋 亮;高橋 亮;Ryo Takahashi;高橋 亮;高橋 亮;木村 海渡; 大竹 優也; 高橋 亮;高橋 亮;高橋 亮;高橋 亮;高橋 亮;大竹 優也; 木村 海渡; 高橋 亮;高橋 亮;木村 海渡; 大竹 優也; 高橋 亮;Hiroki Matsui; Ryo Takahashi;高橋 亮;Mohsen Gheibi; David A. Jorgensen; Ryo Takahashi;高橋 亮;高橋 亮;Ryo Takahashi;高橋 亮;高橋 亮;高橋 亮;Ryo Takahashi;高橋 亮;Olgur Celikbas; Justin Lyle; Ryo Takahashi; Yongwei Yao;Mohsen Gheibi; David A. Jorgensen; Ryo Takahashi;Olgur Celikbas; Ryo Takahashi;Ryo Takahashi;Ryo Takahashi;Ryo Takahashi;高橋 亮;Ryo Takahashi;高橋 亮;高橋 亮;高橋 亮;Irena Peeva - 通讯作者:
Irena Peeva
Applications of mapping cones over Clements–Lindström rings
- DOI:
10.1016/j.jalgebra.2010.10.006 - 发表时间:
2011-01-01 - 期刊:
- 影响因子:
- 作者:
Vesselin Gasharov;Satoshi Murai;Irena Peeva - 通讯作者:
Irena Peeva
Irena Peeva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('Irena Peeva', 18)}}的其他基金
Minimal Free Resolutions and Syzygies
最小的自由分辨率和 Syzygies
- 批准号:
2001064 - 财政年份:2020
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
Homology of Monomial and Toric Ideals
单项式和环面理想的同调
- 批准号:
9970334 - 财政年份:1999
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
相似海外基金
Exploring Frontiers on applying CubeSat images with very high spatial and temporal resolutions to remotely estimate species-level tree phenology
探索应用具有极高空间和时间分辨率的 CubeSat 图像远程估计物种级树木物候的前沿
- 批准号:
23K18517 - 财政年份:2023
- 资助金额:
$ 19.2万 - 项目类别:
Grant-in-Aid for Challenging Research (Exploratory)
Phenomenological inspection of string landscape based on resolutions of singularities
基于奇点解析的弦景观现象学检验
- 批准号:
22KJ1426 - 财政年份:2023
- 资助金额:
$ 19.2万 - 项目类别:
Grant-in-Aid for JSPS Fellows
Resolutions of positivity in Hopf algebras
Hopf 代数中正性的解析
- 批准号:
RGPIN-2020-04230 - 财政年份:2022
- 资助金额:
$ 19.2万 - 项目类别:
Discovery Grants Program - Individual
A graph framework for modelling, analysing, and visualising big geospatial networks at varying spatial resolutions
用于以不同空间分辨率对大型地理空间网络进行建模、分析和可视化的图形框架
- 批准号:
547701-2020 - 财政年份:2022
- 资助金额:
$ 19.2万 - 项目类别:
Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Diagnostics development of ionization states in intense-laser irradiated matter with high spatio-temporal resolutions
高时空分辨率强激光照射物质电离态的诊断进展
- 批准号:
22K03571 - 财政年份:2022
- 资助金额:
$ 19.2万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Finite Group Actions on Free Resolutions
自由解的有限群动作
- 批准号:
2200844 - 财政年份:2022
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
The Balance of Power: Analysis of Interstate Wars and Peaceful Resolutions of Conflict, 1000-2000 AD
权力平衡:对公元 1000-2000 年国家间战争与和平解决冲突的分析
- 批准号:
22K01533 - 财政年份:2022
- 资助金额:
$ 19.2万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
A graph framework for modelling, analysing, and visualising big geospatial networks at varying spatial resolutions
用于以不同空间分辨率对大型地理空间网络进行建模、分析和可视化的图形框架
- 批准号:
547701-2020 - 财政年份:2021
- 资助金额:
$ 19.2万 - 项目类别:
Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Investigations in Combinatorial and Topological Resolutions
组合和拓扑解析的研究
- 批准号:
564650-2021 - 财政年份:2021
- 资助金额:
$ 19.2万 - 项目类别:
University Undergraduate Student Research Awards