Introduction to the Minimal Model Problem

Chapter O. Notation and preliminaries § 0-1.Kleiman's criterion for ampleness § 0-2.Definitions of terminal, canonical and (weak) log-terminal singularities § 0-3.Canonical varieties § 0-4.The minimal model conjecture Chapter 1. Vanishing theorems § 1-1.Covering Lemma § 1-2.Vanishing theorem of Kawamata and Viehweg § 1-3.Vanishing theorem of Elkik and Fujita Chapter 2. Non-Vanishing Theorem § 2-1.Non-Vanishing Theorem Chapter 3. Base Point Free Theorem § 3-1.Base Point Free Theorem § 3-2.Contractions of extremal faces § 3-3.Canonical rings of varieties of general type Chapter 4. Cone Theorem § 4-1.Rationality Theorem § 4-2.The proof of the Cone Theorem Chapter 5. Flip Conjecture § 5-1.Types of contractions of extremal rays § 5-2.Flips of toric morphisms Chapter 6. Abundance Conjecture § 6-1.Nef and abundant divisors