2013/04/05 by Mark Gross, Valentino Tosatti, Yuguang Zhang · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Base (topology) #Calabi–Yau manifold #Fibered knot #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hermitian manifold #Kodaira dimension #Limit (mathematics) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Ricci curvature #Symplectic geometry #Volume form #math.AG #math.DG #math.MG
paper · pdf · doi:10.4310/cag.2016.v24.n1.a4
published as Comm. Anal. Geom. 24 (2016), no.1, 93-113
arxiv created 2013/04/05 · openalex publication_date 2016/01/01 · arxiv updated 2016/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper is a sequel to arXiv:1108.0967. We further study Gromov-Hausdorff collapsing limits of Ricci-flat K"ahler metrics on abelian fibered Calabi-Yau manifolds. Firstly, we show that in the same setup as arXiv:1108.0967, if the dimension of the base manifold is one, the limit metric space is homeomorphic to the base manifold. Secondly, if the fibered Calabi-Yau manifolds are Lagrangian fibrations of holomorphic symplectic manifolds, the metrics on the regular parts of the limits are special K"ahler metrics. By combining these two results, we extend arXiv:math/0008018 to any fibered projective K3 surface without any assumption on the type of singular fibers.