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arXiv · 2609.34382

Splitting the Matroid Determinant

Clara Briand·Leonie Kayser·Julian Weigert
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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.

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Clara Briand, Leonie Kayser, Julian Weigert. 2026-09-28. Splitting the Matroid Determinant. https://arxiv.org/abs/2609.34382

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