Existence and deformations of Kahler-Einstein metrics on smoothable Q-Fano varieties

Abstract

We prove the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable, K-polystable Q-Fano varieties, and we show how these metrics behave, in the Gromov-Hausdorff sense, under Q-Gorenstein smoothings.

References in corpus (2)

• Asymptotically log Fano varieties
• The Continuity Method to Deform Cone Angle

Cited by in corpus (8)

• On the singularity type of full mass currents in big cohomology classes
• On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties
• K-stability of cubic threefolds
• Applications of the moduli continuity method to log K-stable pairs
• On K-stability of some del Pezzo surfaces of Fano index 2
• Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
• Kähler-Einstein metrics on families of Fano varieties
• Weighted cscK metrics on Kähler varieties