Rational quintics in the real plane

TL;DR

This paper classifies generic rational quintic curves in the real projective plane based on their topological properties, contributing to the understanding of real algebraic curves in the context of Hilbert's 16th problem.

Contribution

It provides an isotopy classification of generic rational quintic curves in the real projective plane, extending topological understanding of these algebraic curves.

Findings

Classification of rational quintics in $\

Topological types of generic rational quintics identified

Connection to Hilbert's 16th problem established

Abstract

From a topological viewpoint, a rational curve in the real projective plane is generically a smoothly immersed circle and a finite collection of isolated points. We give an isotopy classification of generic rational quintics in $\mathbb{RP}^2$ in the spirit of Hilbert's 16th problem.