Relative De Rham Complexes, Families of Varieties

相关 De Rham 复合体，品种家族

• 批准号: 9600089
• 负责人: Steven Kleiman
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 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: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9600089&HistoricalAwards=false
• 关键词: Relative; De; Rham; Complexes; Families

Kleiman Kovacs 9600089 This awards supports the research of Dr. S. Kovacs as a post-doctoral associate of Professor S. Kleiman to work on problems in complex algebraic geometry. He hopes to find a construction for the relative De Rham complex for non-smooth morphisms. He also hopes to study log flips of complex varieties and to try to confirm Kollar's conjecture that certain Abelian surfaces blown-up at a single point give cones which decompose into non-trivial finitely generated part and a non-trivial nowhere locally finitely generated part. This research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

Kleiman Kovacs 9600089该奖项支持S. Kovacs博士作为S. Kleiman教授的博士后助理研究复杂代数几何问题。他希望为非光滑态射的相对De Rham复合体找到一种结构。他还希望研究复数的对数翻转，并试图证实科勒的猜想，即某些在单点膨胀的阿贝尔曲面会给出分解成非平凡有限生成部分和非平凡无局部有限生成部分的锥。这项研究属于代数几何领域，是现代数学中最古老的部分之一，但在过去10年里，它发展到解决了几个世纪以来一直存在的问题的程度。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。