A resultant system as the set of coefficients of a single resultant

Abstract

Explicit expressions for polynomials forming a homogeneous resultant system of a set of m+1 homogeneous polynomial equations in n+1<m+1 variables are given. These polynomials are obtained as coefficients of a homogeneous resultant for an appropriate system of n+1 equations in n+1 variables, which is explicitly constructed from the initial system. Similar results are obtained for mixed resultant systems of sets of n + 1 sections of line bundles on a projective variety of dimension n < m. As an application, an algorithm determining whether one of the orbits under an action of an affine irreducible algebraic group on a quasi-affine variety is contained in the closure of another orbit is described.