Abelian Varieties and Their Subvarieties

阿贝尔变种及其亚变种

• 批准号: 9400636
• 负责人: Olivier Debarre
• 金额: $ 6.77万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400636&HistoricalAwards=false
• 关键词: Abelian; Varieties; Their; Subvarieties

Professor Debarre will investigate geometric properties of abelian varieties. In particular, he will study the topology and geometry of covers of abelian varieties of small degree. He also intends to continue his study of the Schottky problem. 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.

Debarre教授将研究阿贝尔簇的几何性质。特别是，他将研究拓扑结构和几何覆盖的阿贝尔品种的小程度。他还打算继续研究肖特基问题。 这是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，但在过去的四分之一个世纪里，它已经有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。 如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。