Polymatroids and moduli of points in flags
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arXiv
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| Format: | Preprint |
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2024
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| author | Gallardo, Patricio González-Anaya, Javier González, José Luis |
| author_facet | Gallardo, Patricio González-Anaya, Javier González, José Luis |
| contents | We introduce and study different compactifications of the moduli space of $n$ distinct weighted labeled points in a flag of affine spaces. We construct these spaces via the weighted and generalized Fulton-MacPherson compactifications of Routis and Kim-Sato. For certain weights, our compactifications are toric and isomorphic to the polypermutohedral and polystellahedral varieties, which arise in the work of Crowley-Huh-Larson-Simpson-Wang and Eur-Larson on polymatroids, a generalization of matroids. Moreover, we show that these toric compactifications have a fibration structure, with fibers isomorphic to the Losev-Manin space, and are related to each other via a geometric quotient. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polymatroids and moduli of points in flags Gallardo, Patricio González-Anaya, Javier González, José Luis Algebraic Geometry Combinatorics 14J10, 05B35, 14M25 (Primary) 14D06, 52C35, 52B12 (Secondary) We introduce and study different compactifications of the moduli space of $n$ distinct weighted labeled points in a flag of affine spaces. We construct these spaces via the weighted and generalized Fulton-MacPherson compactifications of Routis and Kim-Sato. For certain weights, our compactifications are toric and isomorphic to the polypermutohedral and polystellahedral varieties, which arise in the work of Crowley-Huh-Larson-Simpson-Wang and Eur-Larson on polymatroids, a generalization of matroids. Moreover, we show that these toric compactifications have a fibration structure, with fibers isomorphic to the Losev-Manin space, and are related to each other via a geometric quotient. |
| title | Polymatroids and moduli of points in flags |
| topic | Algebraic Geometry Combinatorics 14J10, 05B35, 14M25 (Primary) 14D06, 52C35, 52B12 (Secondary) |
| url | https://arxiv.org/abs/2411.06816 |