Approximation of holomorphic maps from Runge domains to affine algebraic varieties

TL;DR

This paper provides a geometric proof that holomorphic maps from Runge domains to affine algebraic varieties can be approximated by Nash maps and extends this result to broader contexts.

Contribution

It introduces a geometric proof of the approximation theorem and generalizes it beyond initial settings.

Findings

Holomorphic maps from Runge domains can be approximated by Nash maps.

The approximation theorem is extended to more general cases.

Provides a new geometric approach to the approximation problem.

Abstract

We present a geometric proof of the theorem saying that holomorphic maps from Runge domains to affine algebraic varieties admit approximation by Nash maps. Next we generalize this theorem.