Varieties fibered by good minimal models

TL;DR

This paper proves that under certain conditions, the total space of a fibered algebraic variety inherits a good minimal model when the fibers have one, focusing on cases involving the Iitaka fibration and low-dimensional Albanese maps.

Contribution

It establishes new results on the existence of good minimal models for fibered varieties in specific geometric contexts.

Findings

X has a good minimal model when f is the Iitaka fibration.

X has a good minimal model when f is the Albanese map with relative dimension ≤ 3.

The results extend the understanding of minimal models in fibered algebraic varieties.

Abstract

Let f:X->Y be an algebraic fiber space such that the general fiber has a good minimal model. We show that if f is the Iitaka fibration or if f is the Albanese map of relative dimension no more than three, then X has a good minimal model.