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

交换簇模的函数紧化的结构及其关系研究者将继续研究具有半交换群作用的稳定对的模，特别是给出交换簇模的函数紧化的部分。其目的是：得到该空间的结构和肖特基轨迹的闭包位于其中的方式的详细描述；研究该模空间对相对情形和其他群行动的情形的推广。所采用的方法将是代数几何和组合。这项研究是在代数几何领域，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。从古代开始，在20世纪，它见证了新的和强大的方法的发展。它的应用跨越了科学的界限，延伸到物理和密码学等不同的领域。组合数学与计数有关，是大多数数学实际应用的基础。这笔赠款还将支持对新博士生的教育和科学培训。

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.