On the Kodaira dimension of some algebraic fiber spaces

TL;DR

This paper investigates how the positivity of the canonical bundle behaves in algebraic fiber spaces, proving a conjecture that links two important conjectures in algebraic geometry.

Contribution

It proves Schnell's conjecture, establishing the equivalence between the Non-vanishing Conjecture and its generalized form by Campana and Peternell.

Findings

Proves the descent of positivity of the canonical bundle in fiber spaces

Establishes the equivalence of two major conjectures in algebraic geometry

Advances understanding of the structure of algebraic fiber spaces

Abstract

In this paper, we study the descent of positivity of the canonical bundle along fiber spaces. As a consequence, we prove a conjecture of Schnell, establishing the equivalence between the Non-vanishing Conjecture and its generalized version proposed by Campana and Peternell.