Compactification of metric moduli space of $K3$ surfaces

Zexuan Ouyang; Gang Tian

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arXiv · 2512.13315

Compactification of metric moduli space of $K3$ surfaces

Zexuan Ouyang·Gang Tian

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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.

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Zexuan Ouyang, Gang Tian. 2025-12-15. Compactification of metric moduli space of $K3$ surfaces. https://arxiv.org/abs/2512.13315

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