Dilworth truncations and Hadamard products of linear spaces
Combinatorics
2025-08-08 v1 Algebraic Geometry
Metric Geometry
Abstract
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.
Cite
@article{arxiv.2508.04798,
title = {Dilworth truncations and Hadamard products of linear spaces},
author = {Dario Antolini and Sean Dewar and Shin-ichi Tanigawa},
journal= {arXiv preprint arXiv:2508.04798},
year = {2025}
}
Comments
21 pages, 2 figures