Mathematical Sciences: Linear Systems on Higher Dimensional Varieties

该奖项支持L教授的研究。恩托 研究代数几何。 他将研究线性系统， 更高维度的变种他会努力找到最佳的 伴随线性系统的自由性和很满性的判别准则 三个系列。他还将研究伴随的合合 线性级数 这项研究是在代数几何领域，其中一个 现代数学中最古老的部分，但其中一个 在过去的10年里， 已经屹立了几个世纪最初，它把数字 在平面上由最简单的方程定义，即 多项式今天，该领域不仅使用代数方法， 也来自于分析和拓扑学，相反， 广泛应用于这些领域。 此外，它还证明了自己 在物理学、理论计算机、 科学、密码学、编码理论和机器人技术。

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.