Problems In Algebraic Geometry

代数几何问题

• 批准号: 9713149
• 负责人: Robert Lazarsfeld
• 金额: $ 41.58万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9713149&HistoricalAwards=false
• 关键词: Problems; Algebraic; Geometry

Lazarsfeld 9713149 This award supports work on a number of problems in algebraic geometry. The first is to explore the connections between invariants from higher dimensional complex geometry and the rich classical geometry of abelian varieties and Riemann surfaces. The principal investigator also proposes to continue his work on the geometry of irregular varieties, as well as on the problem of trying to find lower bounds on the local positivity of an ample line bundle at a very general point of a smooth projective variety of arbitrary dimension. Finally, he will investigate some questions growing out of a recent observation with Bo Ilic to the effect that if X is a projective variety of dimension n with non-negative cotangent bundle, then the least degree of a projective embedding of X must grow essentially exponentially in n. This is research in the field of algebraic geometry. Algebraic geometry 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.

拉扎斯菲尔德9713149 该奖项支持在代数几何的一些问题的工作。 第一个是探索来自高维复几何的不变量与丰富的阿贝尔簇和Riemann曲面的经典几何之间的联系。 首席研究员还建议继续他的工作几何的不规则品种，以及对问题的尝试找到下界的地方积极的一个丰富的线丛在一个非常一般的点的顺利投影各种任意尺寸。 最后，他将调查一些问题的增长，最近的观察与波伊利奇的效果，如果X是一个投影品种的维数n与非负余切丛，然后最低程度的投影嵌入X必须增长基本上指数n。 这是代数几何领域的研究。 代数几何是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，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。