Year: 2026
Type: preprint
Abstract: We show that the polar degrees of the coordinate-wise inverse of a linear subspace $L \subseteq \mathbb{P}^n$ are given by the coefficients of a substitution of the reduced characteristic polynomial of the associated matroid $\mathrm{M}(L)$. Our proof connects the geometry of conormal varieties of reciprocal linear spaces to the combinatorial conormal fan of $\mathrm{M}(L)$. As a corollary, we settle two open conjectures regarding matroid discriminants.
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: W7166036270