Singularities of the Minimal Model Program.
Kollár, János.
Singularities of the Minimal Model Program. - Cambridge : Cambridge University Press, 2013. - 1 online resource (382 pages) - Cambridge Tracts in Mathematics . - Cambridge tracts in mathematics. .
Includes bibliographical references and index.
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.
9781107309234 1107309239 9781107035348 1107035341 9781139547895 1139547895 9781107314788 110731478X 9781299403185 1299403182 9781107471252 1107471257 9781107307032 1107307031
CL0500000402 Safari Books Online
Singularities (Mathematics)
Algebraic spaces.
Singularités (Mathématiques)
Espaces algébriques.
MATHEMATICS--Geometry--General.
Singularidades (Matemáticas)
Algebraic spaces
Singularities (Mathematics)
Singularität
Algebraischer Raum
QA614.58 .K685 2013
516.353
Singularities of the Minimal Model Program. - Cambridge : Cambridge University Press, 2013. - 1 online resource (382 pages) - Cambridge Tracts in Mathematics . - Cambridge tracts in mathematics. .
Includes bibliographical references and index.
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.
9781107309234 1107309239 9781107035348 1107035341 9781139547895 1139547895 9781107314788 110731478X 9781299403185 1299403182 9781107471252 1107471257 9781107307032 1107307031
CL0500000402 Safari Books Online
Singularities (Mathematics)
Algebraic spaces.
Singularités (Mathématiques)
Espaces algébriques.
MATHEMATICS--Geometry--General.
Singularidades (Matemáticas)
Algebraic spaces
Singularities (Mathematics)
Singularität
Algebraischer Raum
QA614.58 .K685 2013
516.353