English

Compactification of metric moduli space of $K3$ surfaces

Differential Geometry 2025-12-16 v1 Algebraic Geometry Representation Theory

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 hyperk\"ahler metrics on K3 surfaces. As a corollary, we obtain a classification of the Gromov--Hausdorff limits of those hyperk\"ahler K3 surfaces with a fixed complex structure or with a fixed polarization.

Keywords

Cite

@article{arxiv.2512.13315,
  title  = {Compactification of metric moduli space of $K3$ surfaces},
  author = {Zexuan Ouyang and Gang Tian},
  journal= {arXiv preprint arXiv:2512.13315},
  year   = {2025}
}

Comments

42 pages