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

Abel簇及其关系模的函子紧化的结构研究者将继续研究具有半Abel群作用的稳定对的模，特别是给出Abel簇模的函子紧化的部分。 其目标是：为了得到这个空间的结构的详细描述，以及肖特基轨迹的闭包位于其中的方式;为了研究这个模空间到相对情况和其他群作用的情况的推广。 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。 代数几何的主要目的是解决多项式方程。 它始于古代，在世纪，它看到了新的和非常强大的方法的发展。 它的应用跨越了科学的界限，涉及到物理学和密码学等不同的领域。 组合数学涉及计数，是大多数数学实际应用的基础。 该赠款还将支持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.