A non-Archimedean theory of complex spaces and the cscK problem
Differential Geometry
2025-09-22 v2 Algebraic Geometry
Complex Variables
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 K\"ahler manifolds a result of Chi Li, proving that a stronger version of K-stability implies the existence of a unique constant scalar curvature K\"ahler metric.
Cite
@article{arxiv.2409.06221,
title = {A non-Archimedean theory of complex spaces and the cscK problem},
author = {Pietro Mesquita-Piccione},
journal= {arXiv preprint arXiv:2409.06221},
year = {2025}
}
Comments
60 pages. Final version to appear in Advances in Mathematics