Mirror symmetry for singular double cover Calabi--Yau varieties: quantum test
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914078952259584 |
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| author | Lee, Tsung-Ju Lian, Bong H. Yau, Shing-Tung |
| author_facet | Lee, Tsung-Ju Lian, Bong H. Yau, Shing-Tung |
| contents | We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY double covers of \(\mathbb{P}^{3}\) branched along (1) a union of eight hyperplanes in general position, and (2) a union of four hyperplanes and a quartic in generation. Our previous construction produces hypothetical singular mirror partners. We prove that they are mirror pairs in the sense that the \(B\)-model of one (variation of Hodge structure) is equivalent to the \(A\)-model of another (the untwisted part of the genus zero orbifold Gromov--Witten invariants). The technique can be generalized and applied to the case when the nef-partition is trivial. As a byproduct, we also verify Morrison's conjecture in certain circumstances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mirror symmetry for singular double cover Calabi--Yau varieties: quantum test Lee, Tsung-Ju Lian, Bong H. Yau, Shing-Tung Algebraic Geometry Mathematical Physics 14J33, 14N35, 14D07 We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY double covers of \(\mathbb{P}^{3}\) branched along (1) a union of eight hyperplanes in general position, and (2) a union of four hyperplanes and a quartic in generation. Our previous construction produces hypothetical singular mirror partners. We prove that they are mirror pairs in the sense that the \(B\)-model of one (variation of Hodge structure) is equivalent to the \(A\)-model of another (the untwisted part of the genus zero orbifold Gromov--Witten invariants). The technique can be generalized and applied to the case when the nef-partition is trivial. As a byproduct, we also verify Morrison's conjecture in certain circumstances. |
| title | Mirror symmetry for singular double cover Calabi--Yau varieties: quantum test |
| topic | Algebraic Geometry Mathematical Physics 14J33, 14N35, 14D07 |
| url | https://arxiv.org/abs/2510.05470 |