Lagrangian skeleta of very affine complete intersections

Fuente: arXiv
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Main Author: Koževnikov, Danil
Format: Preprint
Published: 2025
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author Koževnikov, Danil
author_facet Koževnikov, Danil
contents 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 $X$. We compute the skeleton of $Z^\circ$ and describe its decomposition into standard pieces that are mirror to toric varieties, which generalises the existing results in the case of hypersurfaces. This set-up was first considered by Batyrev and Borisov, who used combinatorial techniques to construct a mirror pair $(Z,\check{Z})$ of such complete intersections. We use our main result to establish homological mirror symmetry for Batyrev-Borisov pairs in the large-volume limit.
format Preprint
id arxiv_https___arxiv_org_abs_2510_23418
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Lagrangian skeleta of very affine complete intersections
Koževnikov, Danil
Symplectic Geometry
Algebraic Geometry
53D37 (Primary), 14J33 (Secondary)
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 $X$. We compute the skeleton of $Z^\circ$ and describe its decomposition into standard pieces that are mirror to toric varieties, which generalises the existing results in the case of hypersurfaces. This set-up was first considered by Batyrev and Borisov, who used combinatorial techniques to construct a mirror pair $(Z,\check{Z})$ of such complete intersections. We use our main result to establish homological mirror symmetry for Batyrev-Borisov pairs in the large-volume limit.
title Lagrangian skeleta of very affine complete intersections
topic Symplectic Geometry
Algebraic Geometry
53D37 (Primary), 14J33 (Secondary)
url https://arxiv.org/abs/2510.23418