Homological mirror symmetry for projective K3 surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917947967012864 |
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| author | Hacking, Paul Keating, Ailsa |
| author_facet | Hacking, Paul Keating, Ailsa |
| contents | We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3 surface of Picard rank $19$ over the field $\mathbb{C}((q))$ of formal Laurent series. This builds on prior work of Seidel, who proved the theorem in the case of the quartic surface, Sheridan, Lekili--Ueda, and Ganatra--Pardon--Shende. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological mirror symmetry for projective K3 surfaces Hacking, Paul Keating, Ailsa Symplectic Geometry Algebraic Geometry We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3 surface of Picard rank $19$ over the field $\mathbb{C}((q))$ of formal Laurent series. This builds on prior work of Seidel, who proved the theorem in the case of the quartic surface, Sheridan, Lekili--Ueda, and Ganatra--Pardon--Shende. |
| title | Homological mirror symmetry for projective K3 surfaces |
| topic | Symplectic Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2503.05680 |