Amazon cover image
Image from Amazon.com

Singularities of the Minimal Model Program.

By: Contributor(s): Material type: TextTextSeries: Cambridge tracts in mathematicsPublication details: Cambridge : Cambridge University Press, 2013.Description: 1 online resource (382 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781107309234
  • 1107309239
  • 9781107035348
  • 1107035341
  • 9781139547895
  • 1139547895
  • 9781107314788
  • 110731478X
  • 9781299403185
  • 1299403182
  • 9781107471252
  • 1107471257
  • 9781107307032
  • 1107307031
Subject(s): Additional physical formats: Print version:: Singularities of the Minimal Model Program.DDC classification:
  • 516.353
LOC classification:
  • QA614.58 .K685 2013
Other classification:
  • MAT038000
Online resources:
Contents:
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.
Summary: An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library EBSCO Mathematics Available
Total holds: 0

Print version record.

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.

Added to collection customer.56279.3

Powered by Koha