On the irreducibility of multivariate subresultants
Laurent Busé, Carlos D’Andrea · Comptes Rendus Mathématique · 2004
Let P 1 ,…, P n be generic homogeneous polynomials in n variables of degrees d 1 ,…, d n respectively. We prove that if ν is an integer satisfying ∑ i =1 n d i − n +1−min{ d i }< ν , then all multivariate subresultants associated to the family P 1 ,…, P n in degree ν are irreducible. We show that the lower bound is sharp. As a byproduct, we get a formula for computing the residual resultant of ρ - ν + n - 1 n - 1 smooth isolated points in ℙ n - 1 .