The harmonic $2$-forms on $K3$ surfaces converging to a flat $4$-dimensional orbifold
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917508649320448 |
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| author | Hattori, Kota |
| author_facet | Hattori, Kota |
| contents | In this article, we study the asymptotic behavior of harmonic $2$-forms on $K3$ surfaces with Ricci-flat Kähler metrics, where metrics converge to the quotient of a flat $4$-torus by a finite group action. We can show that the space of anti-self-dual harmonic $2$ forms decomposes into two subspaces: one converges to the flat $2$-forms on the quotient of the torus, while the other converges to the first Chern forms of anti-self-dual connections on ALE spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The harmonic $2$-forms on $K3$ surfaces converging to a flat $4$-dimensional orbifold Hattori, Kota Differential Geometry 53C26 In this article, we study the asymptotic behavior of harmonic $2$-forms on $K3$ surfaces with Ricci-flat Kähler metrics, where metrics converge to the quotient of a flat $4$-torus by a finite group action. We can show that the space of anti-self-dual harmonic $2$ forms decomposes into two subspaces: one converges to the flat $2$-forms on the quotient of the torus, while the other converges to the first Chern forms of anti-self-dual connections on ALE spaces. |
| title | The harmonic $2$-forms on $K3$ surfaces converging to a flat $4$-dimensional orbifold |
| topic | Differential Geometry 53C26 |
| url | https://arxiv.org/abs/2512.14125 |