Linearizing Algebraic Matroids
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917277269491712 |
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| author | Rosen, Zvi Sidman, Jessica Theran, Louis |
| author_facet | Rosen, Zvi Sidman, Jessica Theran, Louis |
| contents | Although algebraic matroids were discovered in the 1930s, interest in them was largely dormant until their recent use in applications of algebraic geometry. Because nonlinear algebra is computationally challenging, it is easier to work with an isomorphic linear matroid if one exists. We describe an explicit construction that produces a linear representation over an algebraically closed field of characteristic zero starting with the data used in applications. We will also discuss classical examples of algebraic matroids in the modern language of polynomial ideals, illustrating how the existence of an isomorphic linear matroid depends on properties of the field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linearizing Algebraic Matroids Rosen, Zvi Sidman, Jessica Theran, Louis Commutative Algebra Algebraic Geometry Combinatorics 05B35, 12-08, 14Q99, 13P25 Although algebraic matroids were discovered in the 1930s, interest in them was largely dormant until their recent use in applications of algebraic geometry. Because nonlinear algebra is computationally challenging, it is easier to work with an isomorphic linear matroid if one exists. We describe an explicit construction that produces a linear representation over an algebraically closed field of characteristic zero starting with the data used in applications. We will also discuss classical examples of algebraic matroids in the modern language of polynomial ideals, illustrating how the existence of an isomorphic linear matroid depends on properties of the field. |
| title | Linearizing Algebraic Matroids |
| topic | Commutative Algebra Algebraic Geometry Combinatorics 05B35, 12-08, 14Q99, 13P25 |
| url | https://arxiv.org/abs/2507.07220 |