Collapsing Calabi-Yau fibrations and uniform diameter bounds
arXiv:2101.09787 · doi:10.2140/gt.2023.27.397
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 (9)
- Adiabatic limits of Ricci-flat Kahler metrics
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
- Gromov-Hausdorff collapsing of Calabi-Yau manifolds
- Collapsing of abelian fibred Calabi-Yau manifolds
- Infinite time singularities of the Kähler-Ricci flow
- Riemannian geometry of Kahler-Einstein currents
- Higher-order estimates for collapsing Calabi-Yau metrics
- Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
- On collapsing Calabi-Yau fibrations