Continuity of delta invariants and twisted Kähler--Einstein metrics

Abstract

We show that delta invariant is a continuous function on the big cone. We will also introduce an analytic delta invariant and show its continuity in the Kähler cone, from which we deduce the continuity of the greatest Ricci lower bound. Then building on the work Berman-Boucksom-Jonsson, we obtain a uniform Yau-Tian-Donaldson theorem for twisted Kähler-Einstein metrics in general Kähler classes.

arXiv commentfinal version, an oversight in Section 6.2 fixed

References in corpus (11)

• Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
• A variational approach to the Yau-Tian-Donaldson conjecture
• On the constant scalar curvature Kähler metrics, existence results
• A non-Archimedean approach to K-stability
• Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces
• Optimal destabilization of K-unstable Fano varieties via stability thresholds
• Geodesic rays and stability in the cscK problem
• Openness of uniform K-stability in families of $\mathbb{Q}$-Fano varieties
• On energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri neighborhood
• Optimal lower bounds for Donaldson's J-functional
• Existence of cscK metrics on smooth minimal models

Cited by in corpus (5)

• A quantization proof of the uniform Yau-Tian-Donaldson conjecture
• On the optimal volume upper bound for Kähler manifolds with positive Ricci curvature (with an appendix by Yuchen Liu)
• Openness of uniformly valuative stability on the Kähler cone of projective manifolds
• Openness of uniform K-stability in the Kähler cone
• Valuative invariants with higher moments