Approximation of sets defined by polynomials with holomorphic coefficients
Abstract
Let X be an analytic set defined by polynomials whose coefficients a1,...,as are holomorphic functions. We formulate conditions such that for all sequences a(1,n),...,a(s,n) of holomorphic functions converging locally uniformly to a1,...,as respectively the following holds true. If a(1,n),...,a(s,n) satisfy the conditions then the sequence of the sets Xn obtained by replacing aj by a(j,n) in the polynomials, converge to X.
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