Integro-differential equations and functional analysis

Singularities of discriminant loci of Laurent polynomial systems

I. A. Antipova, S. Yu. Chuvashov

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: We consider a system of $n$ Laurent polynomials in $n$ unknowns with variable complex coefficients. For the reduced discriminant locus of such a system, we study the set of critical points of the Horn–Kapranov parametrization. In a special instance ($n=3$), the set of critical values of the parametrization is investigated. It is proved that the multiple root of the corresponding system is degenerate.

Keywords: Laurent polynomial, discriminant locus, $\mathcal{A}$–discriminant, mixed discriminant, degenerate multiple root.

UDC: 517.55, 512.7

MSC: 32A60, 14B05

Received: 11.09.2024
Revised: 05.11.2024
Accepted: 07.11.2024

Language: English

DOI: 10.26516/1997-7670.2025.52.44