The volume polynomial of lattice polygons
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913546063839232 |
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| author | Soprunov, Ivan Soprunova, Jenya |
| author_facet | Soprunov, Ivan Soprunova, Jenya |
| contents | We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the Heine-Shephard problem for two bodies in the plane. As an application, we show how to construct a pair of planar tropical curves (or a pair of divisors on a toric surface) with given intersection number and self-intersection numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The volume polynomial of lattice polygons Soprunov, Ivan Soprunova, Jenya Algebraic Geometry Combinatorics Metric Geometry Number Theory Primary 52B20, 52A39, Secondary 11H55, 14T10, 14M25 We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the Heine-Shephard problem for two bodies in the plane. As an application, we show how to construct a pair of planar tropical curves (or a pair of divisors on a toric surface) with given intersection number and self-intersection numbers. |
| title | The volume polynomial of lattice polygons |
| topic | Algebraic Geometry Combinatorics Metric Geometry Number Theory Primary 52B20, 52A39, Secondary 11H55, 14T10, 14M25 |
| url | https://arxiv.org/abs/2401.06111 |