Minimal Model Program

最小模型程序

• 批准号: 0701101
• 负责人: James McKernan
• 金额: $ 42.33万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2010-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0701101&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.

首席研究员将开展代数簇的双有理分类研究，该研究最近取得了重大突破。 主要研究者提出证明最小模型程序的其余主要猜想，即最小模型的存在性、丰度猜想、翻转终止以及Alexeev-Borisov关于Fano簇有界性的猜想。代数几何是其中之一。最古老和最具挑战性的数学研究领域，它结合了一些非常经典的几何学，例如圆锥曲线和更现代的代数技术，这些技术最近取得了一些惊人的成功，例如例如怀尔斯关于费马大定理的工作。首席研究员正在准备书中的一个章节，介绍高维几何领域最近一些令人兴奋的工作，其目的是以一种可供广大读者理解的形式传播肖库洛夫的开创性工作。 研究者还将尝试在教学中向本科生和研究生传授一些代数几何方面有趣的研究成果。