Titlebook: Introduction to the Mori Program; Kenji Matsuki Textbook 2002 Springer Science+Business Media New York 2002 Dimension.Grad.algebra.algebra

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Birational Geometry of Toric Varieties,edients of the Mori program at work in terms of the concrete geometry of convex cones, following the paper Reid [5]. It is more of my personal note to his beautiful paper, only to “draw legs on the picture of a snake”

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Introduction: The Tale of the Mori Program,The purpose of this book is to give an introductory and comprehensible account of what we call the ., a program that emerged in the last two decades as an effective approach toward the biregular and/or birational classification theory of higher-dimensional algebraic varieties.

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Logarithmic Category,The purpose of this chapter is to give an introductory account of the . introduced by Iitaka and inspired by the works of Grothendieck [2] and Deligne [l][2][3].

Debate

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Vanishing Theorems,The purpose of this chapter is to present several vanishing theorems of cohomology groups that form the technical backbone of our approach to the Mori program.

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Contraction Theorem,This chapter starts with characterizing in Section 8-1 the . the key geometric operations in the process of the minimal model program, as what we call the . described in terms of the convex geometry of the cone of curves, thanks to the cone theorem of Chapter 7. Their existence is guaranteed by the base point freeness theorem of Chapter 6.

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Overview of the Mori Program, the same time we try to distinguish the remarkable features, such as flips, that are unique to higher dimensions. We will not give any detailed proofs in this chapter. The emphasis is on presenting the global picture at an early stage by taking the reader on a quick roller-coaster ride of the Mori program.

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Birational Relation among Minimal Models,n dimension 2 in a fixed birational equivalence class is unique. This is no longer true in dimension 3 or higher, i.e., there may exist many minimal models in general even in a fixed birational equivalence class, and here arises a need to study the birational relation among them.

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