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.
Perturbation results on the zero-locus of a polynomial
TORRENTE, MARIA LAURA;BELTRAMETTI, MAURO CARLO;SOMMESE, ANDREW JOHN
2017-01-01
Abstract
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.
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