Singularities of the Minimal Model Program.

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Preface; Introduction; 1 Preliminaries; 1.1 Notation and conventions; 1.2 Minimal and canonical models; 1.3 Canonical models of pairs; 1.4 Canonical models as partial resolutions; 1.5 Some special singularities; 2 Canonical and log canonical singularities; 2.1 (Log) canonical and (log) terminal singularities; 2.2 Log canonical surface singularities; 2.3 Ramified covers; 2.4 Log terminal 3-fold singularities; 2.5 Rational pairs; 3 Examples; 3.1 First examples: cones; 3.2 Quotient singularities; 3.3 Classification of log canonical surface singularities; 3.4 More examples.

3.5 Perturbations and deformations4 Adjunction and residues; 4.1 Adjunction for divisors; 4.2 Log canonical centers on dlt pairs; 4.3 Log canonical centers on lc pairs; 4.4 Crepant log structures; 4.5 Sources and springs of log canonical centers; 5 Semi-log canonical pairs; 5.1 Demi-normal schemes; 5.2 Statement of the main theorems; 5.3 Semi-log canonical surfaces; 5.4 Semi-divisorial log terminal pairs; 5.5 Log canonical stratifications; 5.6 Gluing relations and sources; 5.7 Descending the canonical bundle; 6 Du Bois property; 6.1 Du Bois singularities.

6.2 Semi-log canonical singularities are Du Bois7 Log centers and depth; 7.1 Log centers and depth; 7.2 Minimal log discrepancy functions; 7.3 Depth of sheaves on slc pairs; 8 Survey of further results and applications; 8.1 Ideal sheaves and plurisubharmonic funtions; 8.2 Log canonical thresholds and the ACC conjecture; 8.3 Arc spaces of log canonical singularities; 8.4 F-regular and F-pure singularites; 8.5 Differential forms on log canonical pairs; 8.6 The topology of log canonical singularities; 8.7 Abundance conjecture; 8.8 Moduli spaces for varieties.

8.9 Applications of log canonical pairs9 Finite equivalence relations; 9.1 Quotients by finite equivalence relations; 9.2 Descending seminormality of subschemes; 9.3 Descending line bundles to geometric quotients; 9.4 Pro-finite equivalence relations; 10 Ancillary results; 10.1 Birational maps of 2-dimensional schemes; 10.2 Seminormality; 10.3 Vanishing theorems; 10.4 Semi-log resolutions; 10.5 Pluricanonical representations; 10.6 Cubic hyperresolutions; References; Index.

An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.

Includes bibliographical references and index.

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