Mathematical Sciences: Kodaira Dimensions of Fiber Products and the Distribution of Rational Points

数学科学：纤维产品的小平维数和有理点的分布

• 批准号: 9505140
• 负责人: Lucia Caporaso
• 金额: $ 4.63万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505140&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Kodaira; Dimensions; Fiber

Caporaso 9505140 Professor Caporaso will work on two problems in algebraic geometry. She intends to study the Kodaira dimension of fiber products of certain families of curves whose general member is of general type. She will also study the geometry of the universal Picard variety. 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 roboticq. ***

Caporaso 9505140 Caporaso教授将研究代数几何中的两个问题。她打算研究一般成员为一般类型的某些曲线族的纤维积的科代拉维数。她还将研究普遍皮卡品种的几何。 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世纪中却有了革命性的发展。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，在这些领域以及物理学、理论计算机科学和机器人科学中也有应用。 ***