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}
}
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42 pages