Approximation of analytic sets along Nash subvarieties (Q1042751)

The article concerns the approximation of analytic sets \(X\) by algebraic ones \(X_{\nu }\) (precisely by Nash sets) in the sense of convergence of holomorphic chains. The main result is that locally it is possible and, moreover, the convergence preserves the multiplicity of \(X\) and \(X_{\nu }\) at almost all points of a fixed Nash subset \(E\subset X\), i.e., \(\text{mult}_{x}X=\text{mult}_{x}X_{\nu }\) for every \(x\) in a dense open subset of \(E.\)