Topologie et d\'enombrement des courbes alg\'ebriques r\'eelles singuli\`eres

TL;DR

This paper analyzes the topology of singular real algebraic curves on smooth surfaces, providing enumeration and bounds on the number of topological types based on degree in the real projective plane.

Contribution

It introduces methods to classify and bound the topological types of singular real algebraic curves in the projective plane, linking topology with algebraic degree.

Findings

Bounded the number of topological types by degree

Enumerated possible topological configurations of singular curves

Provided new insights into the topology of real algebraic curves

Abstract

We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.