本篇論文從基本的輪胎簇定義談起。而輪胎簇一開始是由仿射輪胎簇著手，接著探討投影輪胎簇並發現投影輪胎簇是由一組仿射輪胎簇黏出來的。這些抽象的代數簇都可以經由具體而簡單的凸組合資料著手構造出來。本篇論文旨在探討對偶空間中的組合資料如何對應到對偶的代數簇。當我們把所有此篇論文前六章中完成的事情複製到對偶空間中時就得到了代數簇上的加洛瓦對應。

Toric variety is a branch of algebraic geometry where combinatorics and algebraic geometry substantiate each other. In this paper we will explore how to construct abstract toric variety that can be described purely by algebraic data without embedding into affine or projective spaces from concrete combinatorial data. Two method will be introduced. The first one uses a polytope and the second one a fan. We will present how to construct a fan associated with a polytope and prove that these two methods yield isomorphic toric varieties. Finally, Galois Correspondence appears when we consider everything we have done in duality.

Acknowledements
Preliminaries
Affine Toric Varieties
Projective Toric Varieties
Abstract Varieties
Group action on Toric Varieties
Hypersurfaces in Toric Varieties