Singular surfaces are mathematical objects that exhibit points where they are not smooth or well-defined. These points, known as singularities, can occur in various forms, such as cusps or self-intersections. Singular surfaces are important in fields like algebraic geometry and topology, where they help researchers understand complex shapes and their properties. In practical applications, singular surfaces can be found in computer graphics and modeling, where they may represent real-world objects with imperfections. Understanding these surfaces allows for better rendering techniques and more accurate simulations in areas like engineering and animation.