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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 52

Singularities of Discriminant Loci of Laurent Polynomial Systems

Author(s)
Irina A. Antipova1, Semyon Yu. Chuvashov1

1Siberian 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
About the Authors

Irina A. Antipova, Dr. Sci. (Phys.-Math.), Prof., Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, iantipova@sfu-kras.ru

Semyon Yu. Chuvashov, Student, Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, simontahkraa@gmail.com

For citation
Antipova I. A., Chuvashov S. Yu. Singularities of Discriminant Loci of Laurent Polynomial Systems. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 52, pp. 44–57.

https://doi.org/10.26516/1997-7670.2025.52.44

Keywords
Laurent polynomial, discriminant locus, A–discriminant, mixed discriminant, degenerate multiple root
UDC
517.55, 512.7
MSC
32A60, 14B05
DOI
https://doi.org/10.26516/1997-7670.2025.52.44
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