Collapsing of K3 Surfaces and Special Kähler Structures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913779789332480 |
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| author | Ouyang, Zexuan |
| author_facet | Ouyang, Zexuan |
| contents | We study the structure of $\mathfrak{M}_2$, the set of half-dimensional collapsing spaces of hyperkähler metrics on K3 surfaces. We show that $\mathfrak{M}_2$ consists precisely of those underlying metric spaces of integral singular special Kähler structures (SKSs) on $ \mathbb{P}^1 $. Furthermore, we establish a bijection between integral singular SKSs on $\mathbb{P}^1 $ and Jacobian elliptic K3 surfaces with a marked holomorphic volume form. Additionally, we compute the number of Jacobian elliptic K3 surfaces that correspond to a given metric on $ \mathbb{P}^1 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Collapsing of K3 Surfaces and Special Kähler Structures Ouyang, Zexuan Differential Geometry Algebraic Geometry We study the structure of $\mathfrak{M}_2$, the set of half-dimensional collapsing spaces of hyperkähler metrics on K3 surfaces. We show that $\mathfrak{M}_2$ consists precisely of those underlying metric spaces of integral singular special Kähler structures (SKSs) on $ \mathbb{P}^1 $. Furthermore, we establish a bijection between integral singular SKSs on $\mathbb{P}^1 $ and Jacobian elliptic K3 surfaces with a marked holomorphic volume form. Additionally, we compute the number of Jacobian elliptic K3 surfaces that correspond to a given metric on $ \mathbb{P}^1 $. |
| title | Collapsing of K3 Surfaces and Special Kähler Structures |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2502.18203 |