On the irreducibility of multivariate subresultants

Abstract

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 $\left(\genfrac{}{}{0ex}{}{\rho -\nu +n-1}{n-1}\right)$ smooth isolated points in $\PP^{n-1}.$

Updated version, 4 pages, to appear in CRAS

References in corpus (1)

• Subresultants and Generic Monomial Bases

Cited by in corpus (1)

• On the irreducibility of the determinant of the matrix of moving planes