On K-stability of Calabi-Yau fibrations

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.

v2: 44 pages, improved presentation

References in corpus (5)

• Supercritical deformed Hermitian-Yang-Mills equation
• A quantization proof of the uniform Yau-Tian-Donaldson conjecture
• Existence of cscK metrics on smooth minimal models
• Moduli theory, stability of fibrations and optimal symplectic connections
• On fibration stability after Dervan-Sektnan and singularities