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在该项目中，Alexeev将继续研究主要偏振品种的模量空间的规范功能压缩，以及类似的圆环和semiabelian Pairs的模量空间。这是代数几何学领域的研究。代数几何形状是现代数学最古老的部分之一，但在过去的25年中，它具有革命性的开花。 它起源于它处理的数字可以通过最简单的方程（即多项式）在平面中定义的数字。 如今，该领域不仅利用了来自代数的方法，还利用了分析和拓扑的方法，相反，在这些领域以及物理，理论计算机科学和机器人技术中找到了应用。