2011/09/14 by H. Auvray, Auvray, Hugues
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1109.3159
openalex publication_date 2011/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a divisor D with simple normal crossings in a compact K "ahler\nmanifold X. We show in this article that a K "ahler metric in an arbitrary\nclass, with constant scalar curvature and cusp singularities along the divisor\nis unique in this class when K[D] is ample. This we do by generalizing Chen's\nconstruction of approximate geodesics in the space of K "ahler metrics, and\nproving an approximate version of the Calabi-Yau theorem, both independently of\nthe ampleness of K[D].\n