Mathematical Sciences: Abelian Varieties and Moduli Spaces of Vector Bundles on Curves

数学科学：曲线上向量丛的阿贝尔簇和模空间

• 批准号: 9203919
• 负责人: Olivier Debarre
• 金额: $ 4.28万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-05-15 至 1994-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203919&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Abelian; Varieties; Moduli

This awards supports the research of Professor O. Debarre to work in algebraic geometry. He will work on the dimension of Schottky problem as well as questions about Prym Varieties including the Torelli problem. He will also work on moduli spaces for semi-stable vector bundles. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover, it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

该奖项支持O教授的研究。德巴尔 研究代数几何。 他将致力于 Schottky问题以及关于Prym簇的问题 包括Torelli的问题 他还将研究模数 半稳定向量丛空间 这项研究是在代数几何领域，其中一个 现代数学中最古老的部分，但其中一个 在过去的10年里， 已经屹立了几个世纪 最初，它把数字 在平面上由最简单的方程定义，即 多项式 今天，该领域使用的方法不仅来自 代数，但也从分析和拓扑学，反过来说，它 广泛应用于这些领域。 此外，它还证明， 它本身在物理学、理论、 计算机科学、密码学、编码理论和机器人技术。