Topics in Algebraic Geometry

代数几何专题

• 批准号: 9970295
• 负责人: Lawrence Ein
• 金额: $ 7.2万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970295&HistoricalAwards=false
• 关键词: Topics; Algebraic; Geometry

9970295This is a project in algebraic geometry. Ein proposes to study complexity questions on computational problems concerning geometric objects defined by a system of algebraic equations. In particular, he plans to study the complexity in finding the relations among the equations that define an irreducible variety. Ein also proposes to study geometric properties of linear systems on algebraic varieties.Algebraic geometry is one of the oldest branches of mathematics. It studies geometric objects defined by algebraic equations. Because of their rich structure and fundamental importance, these geometric objects have been studied extensively by mathematicians. In recent years, mathematicians have found important applications of algebraic geometry to mathematical physics, coding theory, compuatational science, number theory, and topology.

[9970295]这是代数几何中的一个课题。Ein建议研究由代数方程组定义的几何对象的计算问题的复杂性问题。特别是，他计划研究寻找定义不可约变量的方程之间关系的复杂性。Ein还提出研究代数变量上线性系统的几何性质。代数几何是数学最古老的分支之一。它研究由代数方程定义的几何对象。由于其丰富的结构和基本的重要性，这些几何对象已被数学家广泛研究。近年来，数学家发现了代数几何在数学物理、编码理论、计算科学、数论和拓扑学中的重要应用。