Mathematical Sciences: RUI: Geometry of Toric Varieties

点击翻译按钮获取中文摘要

This award supports the research of Professor Cox to work in algebraic geometry. One of the problems that Professor Cox will address will be the issue of assigning a coordinate ring to a toric variety in a natural way. This ring should be a polynomial ring and should depend only on the toric variety and not on a particular projective embedding. Professor Cox has a suggested construction which seems to have many of the needed properties. This research uses the techniques 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 physics, theoretical computer science, and robotics.