A singular curve is a type of mathematical curve that has points where it fails to be smooth or well-defined. These points, known as singular points, can occur where the curve intersects itself or has a cusp. Singular curves are important in algebraic geometry, as they help mathematicians understand the properties and behaviors of more complex shapes. In the study of singular curves, researchers often analyze their equations and the nature of their singularities. This analysis can reveal insights into related topics such as algebraic varieties and topology. Understanding singular curves is essential for advancements in both theoretical and applied mathematics.