Minimal Model Program

首席研究员将对代数变种的二元分类进行研究，最近在这方面取得了引人注目的突破。主要研究人员建议证明极小模型程序的剩余主要猜想，即极小模型的存在性、丰富性猜想、翻转的终止以及Alexeev-Borisv关于Fano变元有界性的猜想。代数几何是数学中最古老和最具挑战性的研究领域之一，它结合了一些非常经典的几何，例如圆锥截面几何和更现代的代数技巧，这些技巧最近取得了一些引人注目的成功，例如Wiles关于Fermat大定理的工作。首席研究人员正在准备一本书的一章，介绍最近在高维几何领域的一些令人兴奋的工作，其目的是以一种广泛的受众可以接触到的形式传播肖库罗夫的开创性工作。这位研究人员还将在他的教学中尝试将一些有趣的代数几何研究传授给本科生和研究生。

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.