Introduction to the log minimal model program for log canonical pairs

Abstract

We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Kollár's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone and contraction theorems for quasi-log varieties, especially, for log canonical pairs.

158 pages. This version is the same as Kyoto-Math 2009-03. It is a completely revised and expanded version of arXiv:0705.2075 and arXiv:0705.2076

References in corpus (12)

• Inversion of adjunction on log canonicity
• Quasi-log varieties
• On existence of log minimal models
• Termination of (many) 4-dimensional log flips
• Finite generation of the log canonical ring in dimension four
• Basic properties of log canonical centers
• Vanishing and injectivity theorems for LMMP
• Effective base point free theorem for log canonical pairs--Kollár type theorem
• Non-vanishing theorem for log canonical pairs
• Base point free theorems--saturation, b-divisors, and canonical bundle formula--
• Vanishing theorems for toric polyhedra
• Notes on the log minimal model program

Cited by in corpus (41)

• Globally $F$-regular and log Fano varieties
• Finite generation of the log canonical ring in dimension four
• Deformations and obstructions of pairs (X,D)
• Some remarks on the minimal model program for log canonical pairs
• Depth of $F$-singularities and base change of relative canonical sheaves
• Log pluricanonical representations and abundance conjecture
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities
• Introduction to the theory of quasi-log varieties
• A transcendental approach to Kollár's injectivity theorem II
• Simple normal crossing Fano varieties and log Fano manifolds
• On isolated log canonical singularities with index one
• Adjoint rings are finitely generated
• Supplements to non-lc ideal sheaves
• Fundamental groups of symplectic singularities
• On the anti-canonical ring and varieties of Fano type
• Fundamental theorems for the log minimal model program
• Hyperbolicity for log canonical pairs and the cone theorem
• Versions of injectivity and extension theorems
• Existence of log canonical closures
• On the semiampleness of the positive part of CKM Zariski decompositions
• Non-vanishing theorem for log canonical pairs
• Notes on the weak positivity theorems
• Fundamental theorems for semi log canonical pairs
• On maximal Albanese dimensional varieties
• Pull-back of quasi-log structures
• The Angehrn-Siu Type Effective Freeness For Quasi-Log Canonical Pairs
• Minimal model theory for log surfaces
• On the F-purity of isolated log canonical singularities
• Log canonical pairs with boundaries containing ample divisors
• Noncommutative rigidity of the moduli stack of stable pointed curves
• A remark on Kovács' vanishing theorem
• A logarithmic $\bar{\partial }$-equation on a compact Kähler manifold associated to a smooth divisor
• On log minimal models and Zariski decompositions II
• Global $F$-splitting of surfaces admitting an int-amplified endomorphim
• Basepoint-free theorem of Reid--Fukuda type for quasi-log schemes
• The K"ahler-Ricci flow with Log Canonical Singularities
• M-regular Decompositions for pushforwards of pluricanonical bundles of pairs to abelian varieties
• On isolated log canonical centers
• The Mukai conjecture for log Fano manifolds
• Factorization of anticanonical maps of Fano type varieties
• Effective base point free theorem for log canonical pairs II--Angehrn--Siu type theorems--