Approximation of sets defined by polynomials with holomorphic coefficients

Details Approximation of sets defined by polynomials with holomorphic coefficients Approximation of sets defined by polynomials with holomorphic coefficients

2007-12-18

arxiv.org/abs/0712.3029v1

Mathematics

Complex Variables

10 pages

Scientific paper

Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to a_1,...,a_s respectively the following holds true. If a_(1,n),...,a_(s,n) satisfy the conditions then the sequence of the sets {X_n} obtained by replacing a_j by a_(j,n) in the polynomials, converge to X.

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