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arXiv · 2510.23418

Lagrangian skeleta of very affine complete intersections

Danil Koževnikov
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Abstract

Let $Z^\circ$ be a complete intersection inside $(\mathbb{C}^*)^n$ that compactifies to a smooth Calabi-Yau subvariety $Z$ inside a Fano toric variety. We compute the Lagrangian skeleton of $Z^\circ$ 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 $(Z,\check{Z})$ 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.

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Danil Koževnikov. 2025-10-27. Lagrangian skeleta of very affine complete intersections. https://arxiv.org/abs/2510.23418

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