Lagrangian skeleta of very affine complete intersections
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917045591867392 |
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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 |