Compactification of metric moduli space of K3 surfaces

2025/12/15 by Zexuan Ouyang, Gang Tian, Ouyang, Zexuan +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2512.13315

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture of Odaka--Oshima, which says that there is an algebraic description of the Gromov--Hausdorff compactification of all unit-diameter hyperkähler metrics on K3 surfaces. As a corollary, we obtain a classification of the Gromov--Hausdorff limits of those hyperkähler K3 surfaces with a fixed complex structure or with a fixed polarization.

Citations

• Collapsing of K3 Surfaces and Special Kähler Structures
• A short proof of the surjectivity of the period map on K3 manifolds
• The Kähler geometry of toric manifolds
• Collapsing geometry of hyperkähler 4-manifolds and applications
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Collapsing Ricci-flat metrics on elliptic K3 surfaces
• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces
• Ergodic complex structures on hyperkahler manifolds: an erratum
• ALF gravitational instantons and collapsing Ricci-flat metrics on the K3\n surface
• Large Complex Structure Limits of K3 Surfaces

Related

• Collapsing K3 Surfaces and Moduli Compactification
• Compact moduli of K3 surfaces
• On the GHKS compactification of the moduli space of K3 surfaces of degree two
• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• The Kummer Construction of Calabi-Yau and Hyper-Kähler Metrics on the K3 Surface, and Large Families of Volume Non-collapsed Limiting Compact Hyper-Kähler Orbifolds