Polynomial systems admitting a simultaneous solution
Commutative Algebra
2025-01-14 v3 Algebraic Geometry
Abstract
We provide a complete description of the ideal that serves as the resultant ideal for n univariate polynomials of degree d. We in particular describe a set of generators of this resultant ideal arising as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalising the classical Sylvester resultant of two polynomials.
Cite
@article{arxiv.2306.02085,
title = {Polynomial systems admitting a simultaneous solution},
author = {Austin Conner and Mateusz Michalek and Michael Schindler and Balazs Szendroi},
journal= {arXiv preprint arXiv:2306.02085},
year = {2025}
}
Comments
9 pages; v2: added some classical references and a new result on projective scheme structure, communicated by Jan Stevens, v3: some further references, version to be published in J. Alg