Mathematical Sciences: Linear Systems on Higher Dimensional Varieties

该奖项支持L.Ein教授在代数几何领域的研究。他将研究高维变种上的线性系统。他将试图为三重的伴随线性级数找到自由性和非常宽泛的最佳判据。他还将研究伴随线性级数的合子。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它发展到了解决了几个世纪以来的问题的地步。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，这个领域不仅使用代数的方法，而且还使用分析和拓扑学的方法，相反，它在这些领域被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。

This awards supports the research of Professor L. Ein to work in algebraic geometry. He will work on linear systems on higher dimensional varieties. He will try to find optimal criteria for freeness and very ampleness for adjoint linear series on threefolds. He will also study syzygies of adjoint linear series. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.