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

Caporaso教授将研究代数几何中的两个问题。她打算研究某些曲线族的纤维产品的Kodaira维数，其一般成员为一般型。她还将研究宇宙皮卡德变体的几何。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25年里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它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得到了应用。＊＊＊

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. ***