Structure of Functorial Compactification of Moduli of Abelian Varieties and their Relatives

阿贝尔簇及其近缘模的函数紧化结构

• 批准号: 0101280
• 负责人: Valery Alexeev
• 金额: $ 33.69万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0101280&HistoricalAwards=false
• 关键词: Structure; Functorial; Compactification; Moduli; Abelian

Structure of functorial compactification ofmoduli of abelian varieties and their relativesThe investigator will continue to study the moduli of stable pairs with semiabelian group action and, in particular, the part which gives the functorial compactification of the moduli of abelian varieties. The aims are: to get a detailed description of the structure of this space and the way the closure of the Schottky locus sits inside of it; to study generalizations of this moduli space to the relative case and to the case of other group actions. The methods employed are going to be both algebro-geometric and combinatorial.This research is in the field of algebraic geometry, but with a strong combinatorial aspect. The main object of algebraic geometry is solutions of polynomial equations. Started in the ancient times, in the 20th century it saw development of new and enormously powerful methods. Its applications reach across the scientific boundaries to such diverse fields as physics and cryptography. Combinatorics concerns counting, and is the basis of most real-life applications of mathematics. The grant will also support education and scientific training of new PhD students.

阿贝尔簇及其相关模的函子紧缩结构研究者将继续研究具有半阿贝尔群作用的稳定对的模，特别是给出阿贝尔簇模的函子紧缩的部分。 目的是：详细描述该空间的结构以及肖特基轨迹闭合在其中的方式；研究该模空间对相关情况和其他群体行为情况的概括。 所采用的方法将是代数几何和组合的。这项研究属于代数几何领域，但具有很强的组合方面。 代数几何的主要目标是多项式方程的解。 它始于古代，在 20 世纪见证了新的、极其强大的方法的发展。 它的应用跨越了科学界限，到达了物理学和密码学等不同领域。 组合数学涉及计数，是大多数现实生活中数学应用的基础。 这笔赠款还将支持新博士生的教育和科学培训。