Approximating curves on real rational surfaces

TL;DR

This paper establishes topological criteria for when simple closed curves on real rational surfaces can be approximated by smooth rational curves, including those with specified self-intersection numbers.

Contribution

It provides necessary and sufficient topological conditions for approximability of curves on real rational surfaces, advancing understanding of curve approximation in algebraic geometry.

Findings

Topological conditions for approximability are characterized.

Approximation criteria include constraints on complex self-intersection numbers.

Results apply to smooth rational curves on real rational surfaces.

Abstract

We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex self-intersection number.