Effective semi-ampleness of Hodge line bundles on curves

TL;DR

This paper proves a special case of the effective semi-ampleness conjecture for certain fibrations over smooth projective curves, advancing understanding of line bundle positivity in algebraic geometry.

Contribution

It establishes the effective semi-ampleness for Q-Gorenstein klt-trivial fibrations over curves with fibers of klt log Calabi-Yau pairs of Fano type, a specific case of a broader conjecture.

Findings

Proves effective semi-ampleness in a special case

Advances understanding of line bundles on fibrations

Supports the conjecture in specific geometric contexts

Abstract

In this note, we prove effective semi-ampleness conjecture due to Prokhorov and Shokurov for a special case, more concretely, for Q-Gorenstein klt-trivial fibrations over smooth projective curves whose fibers are all klt log Calabi-Yau pairs of Fano type.