Collapsing Calabi-Yau fibrations and uniform diameter bounds

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.

References in corpus (3)

• Riemannian geometry of Kahler-Einstein currents
• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• On collapsing Calabi-Yau fibrations

Cited by in corpus (1)

• Ricci-flat metrics on Calabi-Yau manifolds