Mathematical Sciences: Linkage, Symmetric Algebras, and Hyperplane Sections

数学科学：联动、对称代数和超平面截面

• 批准号: 9305832
• 负责人: Bernd Ulrich
• 金额: $ 6万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305832&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Linkage; Symmetric; Algebras

This award supports research in three areas of commutative algebra. The first part of this work is directed at studying linkage. The principal investigator will study a numerical condition on the graded resolution that might imply that an ideal is licci. He also will study the relation between several possible definitions for a local ring to be licci. The second part of his work is concerned with symmetric algebras of modules and Vasconcelos' Factorial Conjecture. The third part of his work is aimed at understanding reduced and irreducible projective curves in terms of their general hyperplane sections. This is reasearch in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origins, 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 theoretical computer science and robotics.

该奖项支持交换代数的三个领域的研究。这项工作的第一部分是针对链接的研究。首席研究员将研究关于分级分辨率的一个数值条件，该条件可能暗示理想是LICI。他还将研究局部环是LICI的几种可能定义之间的关系。他的第二部分工作是关于模上的对称代数和瓦斯康塞洛斯的阶乘猜想。他的工作的第三部分旨在根据一般的超平面截面来理解可约和不可约的射影曲线。这是对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25年里，它取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，这个领域不仅使用代数的方法，而且使用分析和拓扑学的方法，相反，在这些领域以及理论计算机科学和机器人学中找到了应用。