A non-Archimedean theory of complex spaces and the cscK problem

Abstract

In this paper we develop an analogue of the Berkovich analytification for non-necessarily algebraic complex spaces. We apply this theory to generalize to arbitrary compact Kähler manifolds a result of Chi Li, proving that a stronger version of K-stability implies the existence of a unique constant scalar curvature Kähler metric.

60 pages. Final version to appear in Advances in Mathematics

References in corpus (3)

• Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
• Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
• K-semistability of cscK manifolds with transcendental cohomology class