Mathematical Sciences: Research in the Deformation Theory ofSubvarieties of Higher Codimension

该奖项支持在代数几何的研究， 犹他州大学的赫伯特克莱门斯博士。克莱门斯教授 将工作的几何通用五次三倍和 一般性的问题所产生的猜想，这三倍 只能承载1000条有理曲线。技 将使用的是D-理论中的推进结构， 模和无穷小Abel-Jacobi映射等。 这是代数几何领域的研究， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。如今，该领域 使用的方法不仅从代数，但从分析和 拓扑学，反过来说， 以及理论计算机科学和机器人学。

This award supports the research in Algebraic Geometry of Dr. Herbert Clemens of the University of Utah. Professor Clemens will work on the geometry of the generic quintic threefold and on general questions arising from the conjecture that this threefold can carry only finitely many rational curves. Techniques that he will use are the pushforward construction from the theory of D- modules and the infinitesimal Abel-Jacobi map, among others. This is research 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 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 theoretical Computer Science and in Robotics.