這篇碩士論文在學習代數曲面上的Sarkisov Program：即固定兩個Mori fiber spaces間的雙有理映射可拆解成有限多Sarkisov links。從論述過程中，我們可估計所需的Sarkisov links個數上界。針對這個目標，文中介紹解決此問題所需的背景知識(R.Hartshorne撰寫的[Algebraic Geometry]第一到三章和第五章以及K.Matsuki撰寫的[Introduction to the Mori Program]第一章)；此外，我們介紹2維度的Minimal Model Program兩種產物:Minimal model和Mori fiber spaces及其性質。;The motivation of this thesis is to study Sarkisov Program in dimension 2 : any birational map between two Mori fiber spaces can be decomposed into finitely many Sarkisov links. According to the study, we are able to estimate a specific upper bound for the number of Sarkisov links in the program. For this purpose, we give some basic terminologies ([R.Hartshorne, “Algebraic Geometry”] from chapter 1 to chapter 3 and chapter 5, [K.Matsuki, “Introduction to the Mori Program”]chapter 1). In addition, we introduce the minimal model program and some properties of its two outcomes: minimal models and Mori fiber spaces.
