On the irreducibility of multivariate subresultants

Details On the irreducibility of multivariate subresultants On the irreducibility of multivariate subresultants

2003-09-23

arxiv.org/abs/math/0309374v2

Mathematics

Algebraic Geometry

Updated version, 4 pages, to appear in CRAS

Scientific paper

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 $\PP^{n-1}.$

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