Mathematical Sciences: Chow Groups of Smooth Projective Varieties

9306733 Schoen此拨款支持C. Schoen教授研究由高维循环定义的Chow群。他还将研究在实数上定义的代数曲线到零属曲线的映射。这个项目属于算术几何的一般领域，这门学科融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。＊＊＊

9306733 Schoen This grant supports the research of Professor C. Schoen to work on Chow groups defined by cycles of higher dimensions. He will also study maps of an algebraic curve to a genus zero curve defined over the reals. This project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks. ***