Polynomial systems admitting a simultaneous solution

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.

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