Minimal Model Program

最小模型程序

• 批准号: 1054622
• 负责人: James McKernan
• 金额: $ 29.42万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-18 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1054622&HistoricalAwards=false
• 关键词: Minimal; Model; Program

The principal investigator will conduct research on the birational classification of algebraic varieties, in which spectacular breakthroughs have been made recently. The principal investigator proposes to prove the remaining major conjectures of the minimal model program,namely the existence of minimal models, the abundance conjecture, termination of flips, and the conjecture of Alexeev-Borisov concerning boundedness of Fano varieties.Algebraic Geometry is one of the oldest and most challenging of areas of research in mathematics, which combines some very classicial geometry, for example that of conic sections and the more modern techniques of algebra, which have had some recent spectacular successes, for example the work of Wiles on Fermat's Last Theorem. The principal investigator is preparing a chapter of a book on some recent exciting work in higher dimensional geometry, whose aim is to disseminate the seminal work of Shokurov in a form which will be accessible to a wide audience. The investigator will also try to impart some of the interesting research in algebraic geometry to undergraduate and graduate students in his teaching.

首席研究员将进行代数簇的双有理分类的研究，其中最近取得了惊人的突破。 主要研究者提出证明最小模型程序的其余主要命题，即最小模型的存在性，丰度猜想，翻转的终止，以及Alexeev-Borisov关于Fano簇有界性的猜想。代数几何是数学研究中最古老和最具挑战性的领域之一，它结合了一些非常经典的几何，例如，圆锥曲线和更现代的代数技术，最近有一些惊人的成功，例如怀尔斯关于费马大定理的工作。主要研究人员正在准备一本书的一章，一些最近令人兴奋的工作，在高维几何，其目的是传播开创性的工作Shokurov的形式，这将是访问广大观众。 调查员还将试图传授一些有趣的研究代数几何本科生和研究生在他的教学。