On K-stability of Calabi-Yau fibrations

TL;DR

This paper establishes a link between the K-stability of Calabi-Yau fibrations over curves and their base curves, and proves the existence of cscK metrics under certain conditions.

Contribution

It characterizes the uniform K-stability of Calabi-Yau fibrations in terms of the K-stability of base curves and demonstrates the existence of cscK metrics for smooth total spaces.

Findings

Calabi-Yau fibrations over curves are uniformly K-stable iff base curves are K-stable in the log-twisted sense.

Existence of cscK metrics for smooth total spaces of such fibrations.

A precise criterion linking fibration stability to base curve stability.

Abstract

We show that Calabi-Yau fibrations over curves are uniformly K-stable in an adiabatic sense if and only if the base curves are K-stable in the log-twisted sense. Moreover, we prove that there are cscK metrics for such fibrations when the total spaces are smooth.