Collapsing Calabi-Yau fibrations and uniform diameter bounds

TL;DR

This paper investigates the collapsing behavior of Calabi-Yau metrics along fibrations over Riemann surfaces, establishing uniform diameter bounds for fibers and analyzing the geometry near singular fibers.

Contribution

It proves a uniform diameter bound for Calabi-Yau fibers under collapsing, extending previous work to include singular fibers with canonical singularities.

Findings

Established uniform diameter bounds for fibers in collapsing Calabi-Yau fibrations.

Analyzed geometric properties around singular fibers with canonical singularities.

Extended previous results to include cases with singular fibers.

Abstract

As a sequel to \cite{Licollapsing}, we study Calabi-Yau metrics collapsing along a holomorphic fibration over a Riemann surface. Assuming at worst canonical singular fibres, we prove a uniform diameter bound for all fibres in the suitable rescaling. This has consequences on the geometry around the singular fibres.