Classifying terminal Fano varieties using Mirror Symmetry

近年来，出现了两种根本不同的方法来绘制终端法诺三倍景观。一方面，有分级环技术开创了布朗和里德，另一方面是新的想法出现镜像对称，作为开发的科茨，科尔蒂，Kasprzyk等，本文利用这两种方法，结合他们根本不同的数学思想，开始了解终端Fano三倍的分类。主要资源是分级环数据库-候选希尔伯特系列的法诺三倍数据库-和各种分类的晶格多面体。

In recent years, two fundamentally different approaches to mapping the landscape of terminal Fano threefolds have emerged. On the one hand, there are the graded ring techniques pioneered by Brown and Reid; on the other hand are new ideas emerging from Mirror Symmetry, as developed by Coates, Corti, Kasprzyk, etc. This thesis exploits both approaches, combining their fundamentally different mathematical ideas to begin to understand the classification of terminal Fano threefolds. The main resources are the Graded Ring Database -- a database of candidate Hilbert series of Fano threefolds -- and various classifications of lattice polytopes.