Approximation of analytic sets with proper projection by algebraic sets

TL;DR

This paper demonstrates that analytic sets with proper projection over Runge domains can be approximated by algebraic sets, bridging complex analytic and algebraic geometry.

Contribution

It introduces a method to approximate certain analytic sets with algebraic sets when the projection is proper over Runge domains.

Findings

Analytic sets with proper projection can be approximated by algebraic sets.

The approximation applies to sets of pure dimension with proper projection.

The result connects complex analytic sets with algebraic geometry in Runge domains.

Abstract

Let $X$ be an analytic subset of $U\times C^n$ of pure dimension $k$ such that the projection of $X$ onto $U$ is a proper mapping, where $U$ is a Runge domain in $C^k$. We show that $X$ can be approximated by algebraic sets.