Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics

TL;DR

This paper proves the subadditivity of Kodaira dimensions for certain fibrations of threefolds in positive characteristic, extending understanding of algebraic geometry in this setting under specific conditions.

Contribution

It establishes subadditivity of Kodaira dimensions for fibrations of threefolds with possibly singular fibers in positive characteristic, under nefness and semi-ampleness assumptions.

Findings

Subadditivity holds for fibrations with smooth or relatively big fibers.

Results apply to threefolds over fields with characteristic p > 5.

Provides new insights into the geometry of threefolds in positive characteristic.

Abstract

In this paper, we will prove subadditivity of Kodaira dimensions for a fibration with possibly singular geometric generic fiber, under certain nefness and relative semi-ampleness conditions. As an application, for a fibration $f: X \to Y$ of a smooth projective threefold over an algebraically closed field of characteristic $p>5$, under the assumption that $Y$ is of general type and non-uniruled, we prove subadditivity of Kodaira dimensions when general fibers are smooth or when $K_{X/Y}$ is relatively big over $Y$.