Mirror symmetry for tropical hypersurfaces and patchworking
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915640668848128 |
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| author | Matessi, Diego Renaudineau, Arthur |
| author_facet | Matessi, Diego Renaudineau, Arthur |
| contents | In the first part of the paper, we prove a mirror symmetry isomorphism between integral tropical homology groups of a pair of mirror tropical Calabi-Yau hypersurfaces. We then apply this isomorphism to prove that a primitive patchworking of a central triangulation of a reflexive polytope gives a connected real Calabi-Yau hypersurface if and only if the corresponding divisor class on the mirror is not zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mirror symmetry for tropical hypersurfaces and patchworking Matessi, Diego Renaudineau, Arthur Algebraic Geometry Combinatorics 14P25, 14T20 (Primary), 14J33 (Secondary) In the first part of the paper, we prove a mirror symmetry isomorphism between integral tropical homology groups of a pair of mirror tropical Calabi-Yau hypersurfaces. We then apply this isomorphism to prove that a primitive patchworking of a central triangulation of a reflexive polytope gives a connected real Calabi-Yau hypersurface if and only if the corresponding divisor class on the mirror is not zero. |
| title | Mirror symmetry for tropical hypersurfaces and patchworking |
| topic | Algebraic Geometry Combinatorics 14P25, 14T20 (Primary), 14J33 (Secondary) |
| url | https://arxiv.org/abs/2407.13611 |