Rational Curves on Calabi-Yau Manifolds & Linear Series

Calabi-Yau 流形上的有理曲线

• 批准号: 9401547
• 负责人: Geng Xu
• 金额: $ 2.17万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401547&HistoricalAwards=false
• 关键词: Rational; Curves; Calabi; Yau; Manifolds

Professor Xu will work on the geometry and topology of Calabi-Yau manifolds as well as higher dimensional projective varieties. In particular, he wants to study rational curves on Calabi-Yau threefolds. He also intends to work on adjoint linear series and pluricanonical series on projective varieties of higher dimension. Finally, he intends to work on higher dimensional sphere-packing problems. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. Algebraic geometry itself 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.

徐教授将致力于Calabi-Yau流形的几何和拓扑以及高维投影簇。特别是，他想研究卡-丘三重上的有理曲线。他还打算工作的伴随线性系列和pluricanonical系列投影品种的更高的层面。最后，他打算研究高维球填充问题。 这是代数几何领域的研究，但它直接关系到本世纪理论物理学的两个重大进展--量子力学和广义相对论。代数几何本身是现代数学中最古老的部分之一，但在过去的四分之一世纪里，它已经有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。