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

2024/09/10 by Mesquita-Piccione, Pietro · 4 citations
#32P05 #32Q15 #32Q26 #53C55 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.06221

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.

Cited by

• Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties
• Two Calabi-Yau theorems for degenerations of compact Kähler manifolds
• A YTD correspondence for constant scalar curvature metrics
• A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem

Related

• A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem
• On the constant scalar curvature Kähler metrics, general automorphism group
• Variational and non-Archimedean aspects of the Yau--Tian--Donaldson\n conjecture
• Compact Complex Surfaces and Constant Scalar Curvature Kähler Metrics
• Rigidity of complete Kähler-Einstein metrics under cscK perturbations