Flips for 3-folds and 4-folds

Name: Flips for 3-folds and 4-folds
Brand: Oxford University Press
Price: 87.09 EUR
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CORTI ALESSIO(Autor*in)

Oxford University Press

1. Auflage

Erschienen am 28. Juni 2007

200 Seiten

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978-0-19-152471-4 (ISBN)

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Inhalt

Intro
Contents
List of Contributors
1 Introduction
1.1 Minimal models of surfaces
1.2 Higher dimensions and flips
1.3 The work of Shokurov
1.4 Minimal models of 3-folds and 4-folds
1.5 The aim of this book
1.6 Pl flips
1.7 b-divisors
1.8 Restriction and mobile b-divisors
1.9 Pbd-algebras
1.10 Restricted systems and 3-fold pl flips
1.11 Shokurov's finite generation conjecture
1.12 What is log terminal?
1.13 Special termination and reduction to pl flips
1.14 The work of Hacon and M[sup(c)]Kernan: adjoint algebras
1.15 Saturated mobile b-divisors on weak del Pezzo klt surfaces
1.16 The CCS Conjecture
1.17 Kodaira's canonical bundle formula and adjunction
1.18 Finite generation on non-klt surfaces
1.19 The glossary
1.20 The book as a whole
1.21 Termination?
1.22 The work of Siu
1.23 Pre-requisites
2 3-fold flips after Shokurov
2.1 Introduction
2.1.1 Statement and brief history of the problem
2.1.2 Summary of the chapter
2.1.3 Other surveys
2.2 Background
2.2.1 Summary
2.2.2 Discrepancy
2.2.3 Klt and plt
2.2.4 Inversion of adjunction
2.2.5 The flip conjecture
2.2.6 Reduction of klt flips to pl flips
2.2.7 Plan of the proof
2.2.8 Log resolution
2.3 The language of function algebras and b-divisors
2.3.1 Function algebras
2.3.2 b-divisors
2.3.3 Saturated divisors and b-divisors
2.3.4 Mobile b-divisors
2.3.5 Restriction and saturation
2.3.6 Pbd-algebras: terminology and first properties
2.3.7 The limiting criterion
2.3.8 Function algebras and pbd-algebras
2.3.9 The finite generation conjecture
2.3.10 A Shokurov algebra on a curve is finitely generated
2.4 Finite generation on surfaces and existence of 3-fold flips
2.4.1 The finite generation conjecture implies existence of pl flips
2.4.2 Linear systems on surfaces
2.4.3 The finite generation conjecture on surfaces
3 What is log terminal?
3.1 What is log terminal?
3.2 Preliminaries on Q-divisors
3.3 Singularities of pairs
3.4 Divisorially log terminal
3.5 Resolution lemma
3.6 Whitney umbrella
3.7 What is a log resolution?
3.8 Examples
3.9 Adjunction for dlt pairs
3.10 Miscellaneous comments
4 Special termination and reduction to pl flips
4.1 Introduction
4.2 Special termination
4.3 Reduction theorem
4.4 The non-Q-factorial minimal model program
5 Extension theorems and the existence of flips
5.1 Introduction
5.1.1 The conjectures of the MMP
5.1.2 Previous results
5.1.3 Sketch of the proof
5.1.4 Notation and conventions
5.2 The real minimal model program
5.3 Finite generation
5.3.1 Generalities on finite generation
5.3.2 Adjoint algebras
5.3.3 Basic properties of the mobile part
5.4 Multiplier ideal sheaves and extension results
5.4.1 Definition and first properties of multiplier ideal sheaves
5.4.2 Extending sections
5.4.3 The restricted algebra is an adjoint algebra
6 Saturated mobile b-divisors on weak del Pezzo klt Surfaces
6.1 Introduction
6.2 Example
6.3 Preliminaries
6.4 Mobile b-divisors of Iitaka dimension one
7 Confined divisors
7.1 Introduction
7.2 Diophantine approximation and descent
7.3 Confined b-divisors
7.4 The CCS conjecture
7.5 The surface case
7.6 A strategy for the general case
8 Kodaira's Canonical bundle formula and adjunction
8.1 Introduction
8.2 Fujita's canonical bundle formula
8.3 The general canonical bundle formula
8.4 Fibre spaces of log Kodaira dimension 0
8.5 Kawamata's canonical bundle formula
8.6 Adjunction
8.7 Tie breaking
8.8 Log canonical purity
8.9 Ambro's seminormality theorem
8.10 Covering tricks and semipositivity of f[sub(*)]?[sub(X /Y)]
9 Non-klt techniques
9.1 Introduction
9.2 Preliminary
9.2.1 Codimension one adjunction
9.2.2 The discriminant of a log pair
9.3 Non-klt finite generation
10 Glossary
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Bibliography
Index
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