Irreducibility of determinants, and Esterov's conjecture on $\mathscr{A}$-discriminants
Algebraic Geometry
2026-02-17 v2 Combinatorics
Abstract
In the space of square matrices, we characterize row-generated subspaces, on which the determinant is an irreducible polynomial. As a corollary, we characterize square systems of polynomial equations with indeterminate coefficients, whose discriminant is an irreducible hypersurface. This resolves a conjecture of Esterov, and, in a sequel paper, leads to a complete description of components and codimensions for discriminants of square systems of equations.
Keywords
Cite
@article{arxiv.2501.14628,
title = {Irreducibility of determinants, and Esterov's conjecture on $\mathscr{A}$-discriminants},
author = {Vladislav Pokidkin},
journal= {arXiv preprint arXiv:2501.14628},
year = {2026}
}
Comments
This preprint is contained in the new version of "Components of discriminants for systems of equations and irreducibility of determinants" (arXiv:2501.15832)