Moduli Spaces of Toric and Abelian Pairs

Alexeev 9870062在这个项目中，Alexeev将继续研究主极化簇的模空间的正则函子紧化，以及复曲面和半交换对的相似模空间。这是代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。 在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。 如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。

Alexeev9870062In this project, Alexeev will continue investigating the canonical functorial compactification of the moduli space of principally polarized varieties, and similar moduli spaces of toric and semiabelian pairs. This is research in the field of algebraic geometry. Algebraic geometry is 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.