Note on quasi-numerically positive log canonical divisors

TL;DR

This paper introduces a subconjecture related to quasi-numerically positive log canonical divisors, demonstrating its implications for the semiampleness conjecture and proving semiampleness in specific elementary cases.

Contribution

It proposes a new subconjecture that links to the semiampleness conjecture and verifies semiampleness in certain basic scenarios.

Findings

Proposes a subconjecture implying the semiampleness conjecture.

Establishes semiampleness in some elementary cases.

Connects quasi-numerically positive divisors to broader conjectures.

Abstract

We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.