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arXiv · 2407.13611

Mirror symmetry for tropical hypersurfaces and patchworking

Diego Matessi·Arthur Renaudineau
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Abstract

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.

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Diego Matessi, Arthur Renaudineau. 2024-07-18. Mirror symmetry for tropical hypersurfaces and patchworking. https://doi.org/10.1017/s1474748025101011

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