Introduction to Symbolic-Numeric Computational Algebra (Lecture 4)
On the explicit continuity of the zero set of a system of complex polynomials

The practical problem studied in my previous lecture will motivate the study of the continuity (for the Hausdorff distance), with respect to the coefficients, of the zero set of a system of complex polynomials with a given pattern and when the Hilbert polynomial of the generated ideal is fixed. This will generalize Ostrowski's continuity results from the univariate to the multivariate case.