Mathematical Sciences: Algebraic Varieties, Birational Geometry and the Structure of the Galois Groups

数学科学：代数簇、双有理几何和伽罗瓦群的结构

• 批准号: 9500774
• 负责人: Fedor Bogomolov
• 金额: $ 8.27万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500774&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Varieties; Birational

This supports the work of Professor Fedor Bogomolov to work on the geometry of algebraic varieties and related problems in birational geometry. He proposes to work on constructing minimal dominant classes of algebraic varieties, asymptotic formulas for cohomology of lines bundles and a counter-example to Lang's conjecture in higher dimensions. He also wants to work on the Sylow subgroups of Galois Groups of certain function fields. This is research in the field of algebraic geometry, yet it directly connects to one of the greatest advances made in the solution of equations--Galois theory. Algebraic geometry itself 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.

这支持了费多尔·博戈莫洛夫教授在代数簇几何和双有理几何中的相关问题上的工作。他建议工作建设最小主导类的代数品种，渐近公式的上同调线束和一个反例郎猜想在更高的层面。他还希望工作的西洛小组的伽罗瓦集团的某些职能领域。 这是在代数几何领域的研究，但它直接连接到一个最伟大的进展，在解决方程-伽罗瓦理论。代数几何本身是现代数学中最古老的部分之一，但在过去的四分之一世纪里，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。