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PreprintCC BY 4.0arXiv

Splitting the Matroid Determinant

  • Clara Briand
  • Leonie Kayser
  • Julian Weigert
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Abstract

The principal matroid determinant EL of a linear space L ⊆ ℙn 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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Cite

BibTeXRIS
BibTeX
@misc{briand2026splitting,
  title = {{Splitting the Matroid Determinant}},
  author = {Clara Briand and Leonie Kayser and Julian Weigert},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34382},
  eprint = {2609.34382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34382},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Splitting the Matroid Determinant
AU  - Clara Briand
AU  - Leonie Kayser
AU  - Julian Weigert
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34382
UR  - https://arxiv.org/abs/2609.34382
AB  - The principal matroid determinant E_L of a linear space L ⊆ 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.
ER  -