Approximation of sets defined by polynomials with holomorphic coefficients
Volume 105 / 2012
Annales Polonici Mathematici 105 (2012), 199-207
MSC: Primary 32C25.
DOI: 10.4064/ap105-2-7
Abstract
Let $X$ be an analytic set defined by polynomials whose coefficients $a_1,\ldots,a_s$ are holomorphic functions. We formulate conditions on sequences $\{a_{1,\nu}\},\ldots,\{a_{s,\nu}\}$ of holomorphic functions converging locally uniformly to $a_1,\ldots,a_s,$ respectively, such that the sequence $\{X_{\nu}\}$ of sets obtained by replacing $a_j$'s by $a_{j,\nu}$'s in the polynomials converges to $X.$
