Multivariate Subresultants in Roots

We give rational expressions for the subresultants of n+1 generic polynomials f_1,..., f_{n+1} in n variables as a function of the coordinates of the common roots of f_1,..., f_n and their evaluation in f_{n+1}. We present a simple technique to prove our results, giving new proofs and generalizing the classical Poisson product formula for the projective resultant, as well as the expressions of Hong for univariate subresultants in roots.