Log pluricanonical representations and abundance conjecture

TL;DR

This paper proves the finiteness of log pluricanonical representations for certain pairs and explores implications for the semi-ampleness of log canonical divisors, advancing the understanding of the abundance conjecture.

Contribution

It establishes the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample divisors and links semi-ampleness properties between pairs and their normalizations.

Findings

Finiteness of log pluricanonical representations proven.

Semi-ampleness of log canonical divisors characterized via normalization.

Several applications to the abundance conjecture provided.

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.