MIRROR SYMMETRY FOR TROPICAL HYPERSURFACES AND PATCHWORKING
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.
Authors
- Diego Matessi (ORCID: https://orcid.org/0000-0002-4603-2214)
- Arthur Renaudineau
Institutions
- University of Milan (IT)
- Université de Lille (FR)
Publication Details
- Journal
- Journal of the Institute of Mathematics of Jussieu
- Published
- 2025-06-11
- DOI
- https://doi.org/10.1017/s1474748025101011
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Université de Lille
- Agence Nationale de la Recherche
- Ministero dell'Università e della Ricerca
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni