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.

Abelian品种及其相对研究者的功能紧凑型结构将继续研究稳定对的稳定对模量，并尤其是semiabelian群体作用，尤其是赋予Abelian品种模量的功能压实的部分。 目的是：详细描述该空间的结构以及Schottky基因座的封闭方式位于其内部；研究该模量空间对相对情况和其他小组行动的概括。 所采用的方法将是代数几何和组合。这项研究在代数几何学领域，但具有很强的组合方面。 代数几何形状的主要对象是多项式方程的解决方案。 始于远古时代，在20世纪，它看到了新的和极大的方法的发展。 它的应用在科学界限到物理和加密等各种领域的界限。 Combinatorics涉及计数，并且是数学大多数现实生活应用的基础。 该赠款还将支持新博士生的教育和科学培训。