Dilworth truncations and Hadamard products of linear spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912524817924096 |
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| author | Antolini, Dario Dewar, Sean Tanigawa, Shin-ichi |
| author_facet | Antolini, Dario Dewar, Sean Tanigawa, Shin-ichi |
| contents | As a direct application of Dilworth truncations of polymatroids, we give short proofs of two theorems: Bernstein's characterisation of algebraic matroids coming from the Hadamard product of two linear spaces, and a formula for the dimension of the amoeba of a complex linear space by Draisma, Eggleston, Pendavingh, Rau, and Yuen. We disprove Bernstein's conjecture on a characterisation of the algebraic matroids of Hadamard products of more than two linear spaces, by giving explicit counterexamples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dilworth truncations and Hadamard products of linear spaces Antolini, Dario Dewar, Sean Tanigawa, Shin-ichi Combinatorics Algebraic Geometry Metric Geometry 05B35 (Primary) 52C25, 14M99, 14N10 (Secondary) As a direct application of Dilworth truncations of polymatroids, we give short proofs of two theorems: Bernstein's characterisation of algebraic matroids coming from the Hadamard product of two linear spaces, and a formula for the dimension of the amoeba of a complex linear space by Draisma, Eggleston, Pendavingh, Rau, and Yuen. We disprove Bernstein's conjecture on a characterisation of the algebraic matroids of Hadamard products of more than two linear spaces, by giving explicit counterexamples. |
| title | Dilworth truncations and Hadamard products of linear spaces |
| topic | Combinatorics Algebraic Geometry Metric Geometry 05B35 (Primary) 52C25, 14M99, 14N10 (Secondary) |
| url | https://arxiv.org/abs/2508.04798 |