Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912647636582400 |
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| author | Bauermeister, Friedrich Hanlon, Andrew Painter, Davis Shaikh, Sair Singer, Benjamin |
| author_facet | Bauermeister, Friedrich Hanlon, Andrew Painter, Davis Shaikh, Sair Singer, Benjamin |
| contents | We show that strata of oriented toric hyperplane arrangements are in bijection with a collection of lattice points in a zonotope. Moreover, we relate the dimension of the stratum and the dimension of the minimal face of the zonotope containing the corresponding lattice point. We discuss how this correspondence is related to toric varieties and the Bondal-Thomsen generators of their derived categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection Bauermeister, Friedrich Hanlon, Andrew Painter, Davis Shaikh, Sair Singer, Benjamin Combinatorics Algebraic Geometry 52B20, 52C35, 05E14, 14M25 We show that strata of oriented toric hyperplane arrangements are in bijection with a collection of lattice points in a zonotope. Moreover, we relate the dimension of the stratum and the dimension of the minimal face of the zonotope containing the corresponding lattice point. We discuss how this correspondence is related to toric varieties and the Bondal-Thomsen generators of their derived categories. |
| title | Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection |
| topic | Combinatorics Algebraic Geometry 52B20, 52C35, 05E14, 14M25 |
| url | https://arxiv.org/abs/2507.14356 |