| Summary: | 碩士 === 國立中央大學 === 數學系 === 106 === 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.
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