Work

Mirror Symmetry for Tropical Hypersurfaces and Patchworking

Year: 2025

Type: article

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.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748025101011

Authors: Diego Matessi, Arthur Renaudineau

Institutions: University of Milan, Université de Lille

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550