Multivariate subresultants in roots

We give a rational expression for the subresultants of n+1 generic polynomials f1,…,fn+1 in n variables as a function of the coordinates of the common roots of f1,…,fn and their evaluation in fn+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.