2025/10/16 by Patrick Graf, Graf, Patrick, Aryaman Patel +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2510.15039
openalex publication_date 2025/10/16 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28
We prove an equivalence between two approaches to characterizing complex-projective varieties X with klt singularities and ample canonical divisor that are uniformized by bounded symmetric domains. In order to do so, we show how to construct a uniformizing variation of Hodge structure from a slope zero tensor and vice versa. As a consequence, we generalize various uniformization results of Catanese and Di Scala to the singular setting. For example, we prove that X is a quotient of a bounded symmetric domain of tube type by a group acting properly discontinuously and freely in codimension one if and only if X admits a slope zero tensor. As a key step in the proof, we establish the compactness of the holonomy group of the singular Kähler--Einstein metric on Xreg.