Moduli Spaces of Toric and Abelian Pairs

环面和阿贝尔对的模空间

• 批准号: 9870062
• 负责人: Valery Alexeev
• 金额: $ 7.47万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2002-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870062&HistoricalAwards=false
• 关键词: Moduli; Spaces; Toric; Abelian; Pairs

Alexeev9870062In this project, Alexeev will continue investigating the canonical functorial compactification of the moduli space of principally polarized varieties, and similar moduli spaces of toric and semiabelian pairs. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.

Alexeev9870062在这个项目中，Alexeev将继续研究主极化簇的模空间以及环面和半交换对的相似模空间的正则函子紧化。这是在代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。