Canonical forms of oriented matroids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912729174900736 |
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| author | Eur, Christopher Lam, Thomas |
| author_facet | Eur, Christopher Lam, Thomas |
| contents | Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full-dimensional projective polytope is a positive geometry. Motivated by the canonical forms of polytopes, we construct a canonical form for any tope of an oriented matroid, inside the Orlik--Solomon algebra of the underlying matroid. Using these canonical forms, we construct bases for the Orlik--Solomon algebra of a matroid, and for the Aomoto cohomology. These bases of canonical forms are a foundational input in the theory of matroid amplitudes introduced by the second author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20782 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical forms of oriented matroids Eur, Christopher Lam, Thomas Combinatorics Algebraic Geometry Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full-dimensional projective polytope is a positive geometry. Motivated by the canonical forms of polytopes, we construct a canonical form for any tope of an oriented matroid, inside the Orlik--Solomon algebra of the underlying matroid. Using these canonical forms, we construct bases for the Orlik--Solomon algebra of a matroid, and for the Aomoto cohomology. These bases of canonical forms are a foundational input in the theory of matroid amplitudes introduced by the second author. |
| title | Canonical forms of oriented matroids |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2502.20782 |