PreprintCC BY 4.0arXiv
Polar Degrees of Matroids
Abstract
We show that the polar degrees of the coordinate-wise inverse of a linear subspace L ⊆ ℙn are given by the coefficients of a substitution of the reduced characteristic polynomial of the associated matroid M(L). Our proof connects the geometry of conormal varieties of reciprocal linear spaces to the combinatorial conormal fan of M(L). As a corollary, we settle two open conjectures regarding matroid discriminants.
Related
BibTeX
@misc{briand2026polar,
title = {{Polar Degrees of Matroids}},
author = {Clara Briand and Leonie Kayser and Julian Weigert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.26281},
eprint = {2606.26281},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26281},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polar Degrees of Matroids
AU - Clara Briand
AU - Leonie Kayser
AU - Julian Weigert
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2606.26281
UR - https://arxiv.org/abs/2606.26281
AB - We show that the polar degrees of the coordinate-wise inverse of a linear subspace L ⊆ ℙ^n are given by the coefficients of a substitution of the reduced characteristic polynomial of the associated matroid M(L). Our proof connects the geometry of conormal varieties of reciprocal linear spaces to the combinatorial conormal fan of M(L). As a corollary, we settle two open conjectures regarding matroid discriminants.
ER -