One base point free theorem for weak log Fano threefolds

TL;DR

This paper proves that for certain weak log Fano threefolds with log canonical pairs, the linear system associated with the anti-canonical divisor becomes free for large multiples, extending base point free results.

Contribution

It establishes a base point free theorem for a special class of weak log Fano threefolds with log canonical singularities.

Findings

Linear system |-n(K_X + D)| is free for large n in the specified class

Extends base point free theorems to certain log canonical threefolds

Provides conditions under which the anti-canonical linear system is base point free

Abstract

Let $(X,D)$ be log canonical pair such $\dim X = 3$ and the divisor $-(K_X + D)$ is nef and big. For a special class of such $(X,D)$'s we prove that the linear system $|-n(K_{X}+D)|$ is free for $n \gg 0$.