  Darboux transformations for polynomial perturbations of a real multivariate
measure are found. The 1D Christoffel formula is extended to the
multidimensional realm: multivariate orthogonal polynomials are expressed in
terms of last quasi-determinants and sample matrices. The coefficients of these
matrices are the original orthogonal polynomials evaluated at a set of nodes,
which is supposed to be poised. A discussion for the existence of poised sets
is given in terms of algebraic hypersufaces in the complex affine space.
