Algebraic Varieties, Birational Geometry and the Structure of the Galois Groups

代数簇、双有理几何和伽罗瓦群的结构

• 批准号: 9801591
• 负责人: Fedor Bogomolov
• 金额: $ 9.32万
• 依托单位: New York University
• 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 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801591&HistoricalAwards=false
• 关键词: Algebraic; Varieties; Birational; Geometry; Structure

Bogomolov 9801591 The principal investigator intends to continue his work on the geometry of algebraic varieties, the structure of Galois groups, and related problems in birational geometry. He plans to work on constructing minimal dominant classes of algebraic varieties, asymptotic formulas for cohomology of line bundles, the description of fundamental groups and universal coverings of algebraic and symplectic manifolds, and the structure of complex symplectic and hyperkahler manifolds. He also proposes to work on the structure of Sylow subgroups of the Galois groups and on the effective version of the stabilization procedure for group cohomology. 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.

Bogomolov 9801591 首席研究员打算继续他在代数簇几何、伽罗瓦群结构以及双有理几何相关问题方面的工作。他计划致力于构造代数簇的最小主导类、线束上同调的渐近公式、基本群的描述和代数和辛流形的通用覆盖，以及复辛和超卡勒流形的结构。他还建议研究伽罗瓦群的 Sylow 子群的结构以及群上同调稳定过程的有效版本。 这是代数几何领域的研究。 代数几何是现代数学最古老的部分之一，但在过去的四分之一个世纪里得到了革命性的发展。在它的起源中，它处理可以通过最简单的方程（即多项式）在平面上定义的图形。如今，该领域不仅使用代数方法，还使用分析和拓扑方法，相反，它正在这些领域以及物理学、理论计算机科学和机器人技术中得到应用。