Higher Dimensional Geometry

高维几何

• 批准号: 9622443
• 负责人: James McKernan
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622443&HistoricalAwards=false
• 关键词: Higher; Dimensional; Geometry

McKernan The area of the planned research is in higher dimensional algebraic geometry, more especially the minimal model program and Mori theory. Building on previous work, some questions centered around the log category (projective varieties with boundaries), especially work on log del Pezzo surfaces and deformation theory. Some more general problems in higher dimensional algebraic geometry are also proposed. 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.

麦科南计划研究的领域是高维代数几何，尤其是最小模型程序和Mori理论。在前人工作的基础上，一些问题集中在对数范畴(有边界的射影簇)上，特别是关于log del Pezzo曲面和形变理论的工作。文中还提出了高维代数几何中一些更一般的问题。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。