English

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.

Keywords

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

R2 v1 2026-06-28T10:55:25.550Z