Let $P_1,...,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,...,d_n$ respectively. We prove that if $\nu$ is an integer satisfying ${ \sum_{ i=1}^n d_i}-n+1-\min\{ d_i\}<\nu,$ then all multivariate subresultants associated to the family $P_1,...,P_n$ in degree $\nu$ are irreducible. We show that the lower bound is sharp. As a byproduct, we get a formula for computing the residual resultant of $\binom{ \rho-\nu +n-1}{ n-1}$ smooth isolated points in $\PP^{ n-1}.$
Categories: math.AG math.AC