2025/10/27 by Danil Koževnikov, Koževnikov, Danil · 1 voice
Mathematics · #math.SG #math.AG
paper · pdf · doi:10.48550/arxiv.2510.23418
Let Z^∘ be a complete intersection inside (ℂ^*)n that compactifies to a smooth Calabi-Yau subvariety Z inside a Fano toric variety. We compute the Lagrangian skeleton of Z^∘ and describe its decomposition into standard pieces that are mirror to toric varieties. This set-up was first considered by Batyrev and Borisov, who used combinatorial techniques to construct a mirror pair (Z,\checkZ) of Calabi-Yau complete intersections in Fano toric varieties. We apply our main result to establish homological mirror symmetry for Batyrev-Borisov pairs in the large-volume limit. We also prove that the equivalence is compatible with toric HMS, along with further functoriality properties with respect to certain natural inclusions of very affine complete intersections.