Log pluricanonical representations and abundance conjecture

Abstract

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is semi-ample if and only if so is the log canonical divisor of its normalization. We also treat many other applications.

35 pages, v2: minor modifications, v3: major revised

References in corpus (5)

• Introduction to the log minimal model program for log canonical pairs
• On Finiteness of B-representation and Semi-log Canonical Abundance
• On isolated log canonical singularities with index one
• Extension theorems, Non-vanishing and the existence of good minimal models
• Existence of log canonical closures

Cited by in corpus (7)

• Some remarks on the minimal model program for log canonical pairs
• On Finiteness of B-representation and Semi-log Canonical Abundance
• Existence of log canonical closures
• Fundamental theorems for semi log canonical pairs
• Existence of log canonical flips and a special LMMP
• On log minimal models and Zariski decompositions II
• Surfaces of globally $F$-regular and $F$-split type