On real Calabi-Yau threefolds twisted by a section
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913237768863744 |
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| author | Matessi, Diego |
| author_facet | Matessi, Diego |
| contents | We study the mod $2$ cohomology of real Calabi-Yau threefolds given by real structures which preserve the torus fibrations constructed by Gross. We extend the results of Castaño-Bernard-Matessi and Arguz-Prince to the case of real structures twisted by a Lagrangian section. In particular we find exact sequences linking the cohomology of the real Calabi-Yau with the cohomology of the complex one. Applying SYZ mirror symmetry, we show that the connecting homomorphism is determined by a ``twisted squaring of divisors'' in the mirror Calabi-Yau, i.e. by $D \mapsto D^2 + DL$ where $D$ is a divisor in the mirror and $L$ is the divisor mirror to the twisting section. We use this to find an example of a connected $(M-2)$-real quintic threefold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On real Calabi-Yau threefolds twisted by a section Matessi, Diego Algebraic Geometry Symplectic Geometry 14P25, 14J33, 53D12 We study the mod $2$ cohomology of real Calabi-Yau threefolds given by real structures which preserve the torus fibrations constructed by Gross. We extend the results of Castaño-Bernard-Matessi and Arguz-Prince to the case of real structures twisted by a Lagrangian section. In particular we find exact sequences linking the cohomology of the real Calabi-Yau with the cohomology of the complex one. Applying SYZ mirror symmetry, we show that the connecting homomorphism is determined by a ``twisted squaring of divisors'' in the mirror Calabi-Yau, i.e. by $D \mapsto D^2 + DL$ where $D$ is a divisor in the mirror and $L$ is the divisor mirror to the twisting section. We use this to find an example of a connected $(M-2)$-real quintic threefold. |
| title | On real Calabi-Yau threefolds twisted by a section |
| topic | Algebraic Geometry Symplectic Geometry 14P25, 14J33, 53D12 |
| url | https://arxiv.org/abs/2302.05357 |