Introduction to the log minimal model program for log canonical pairs

2009/07/09 by Osamu Fujino, Fujino, Osamu · 12 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0907.1506

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.

Cited by

• Factorization of anticanonical maps of Fano type varieties
• The Mukai conjecture for log Fano manifolds
• Log pluricanonical representations and abundance conjecture
• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities
• Notes on the weak positivity theorems
• Log canonical pairs with boundaries containing ample divisors
• On the anti-canonical ring and varieties of Fano type
• The K"ahler-Ricci flow with Log Canonical Singularities
• A logarithmic ∂-equation on a compact Kähler manifold associated to a smooth divisor
• Noncommutative rigidity of the moduli stack of stable pointed curves
• Fundamental theorems for semi log canonical pairs
• Adjoint rings are finitely generated
• Existence of log canonical closures

Related

• Introduction to the theory of quasi-log varieties
• Minimal models of semi-log-canonical pairs
• Minimal model theory for relatively trivial log canonical pairs
• Fundamental theorems for semi log canonical pairs
• The LMMP for log canonical 3-folds in char p