Compactification of metric moduli space of $K3$ surfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915675968110592 |
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| author | Ouyang, Zexuan Tian, Gang |
| author_facet | Ouyang, Zexuan Tian, Gang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compactification of metric moduli space of $K3$ surfaces Ouyang, Zexuan Tian, Gang Differential Geometry Algebraic Geometry Representation Theory 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. |
| title | Compactification of metric moduli space of $K3$ surfaces |
| topic | Differential Geometry Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2512.13315 |