Year: 2026
Type: preprint
Abstract: The principal matroid determinant $E_L$ of a linear space $L \subseteq \mathbb{P}^n$ has been introduced in recent work by Matsubara-Heo and Telen. In this paper, we give the complete factorization of this polynomial into its irreducible components, proving a conjecture of the aforementioned authors. Our methods rely on bounding local multiplicities and an étale-local description of the strata of reciprocal linear spaces developed by Elias, Proudfoot and Wakefield. We also discuss analogous questions for other coordinate-wise powers of linear spaces.
Source: arXiv (Cornell University)
Authors: Briand, Clara, Kayser, Leonie, Weigert, Julian
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5893294622, Positive Geometrie
OpenAlex ID: W7214720219