Mirror symmetry for tropical hypersurfaces and patchworking
arXiv:2407.13611 · doi:10.1017/S1474748025101011
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.
42 pages, 8 figures