Perturbation results on the zero-locus of a polynomial.

Let f and g be complex multivariate polynomials of the same degree. Extending Beauzamy's results which hold in the univariate case, we bound the Euclidean distance of points belonging to the zero-loci of f and g in terms of the Bombieri norm of the difference g−f. We also discuss real perturbations of real polynomials.