Note on rational 1-dimensional compact cycles

TL;DR

This paper proves that the set of rational 1-dimensional cycles in a complex space forms a closed analytic subset within the space of all such cycles.

Contribution

It provides a proof that the subset of rational curves is a closed analytic subset in the cycle space of a complex space.

Findings

Rational curves form a closed analytic subset in the cycle space.

The proof advances understanding of the structure of cycle spaces.

Supports further research in complex geometry and cycle theory.

Abstract

We give a proof of the fact tha the subset of the rational curves form a closed analytic subset in the space of the 1-dimensional cycles of a complex space.