Cubic hypersurfaces are a type of geometric object defined in higher-dimensional spaces, specifically as the zero set of a polynomial equation of degree three. In an n-dimensional space, a cubic hypersurface can be represented by an equation of the form P(x_1, x_2, \ldots, x_n+1) = 0 , where P is a homogeneous polynomial of degree three. These hypersurfaces are significant in algebraic geometry and are studied for their properties and relationships with other geometric structures. They can be analyzed using tools from topology, algebraic geometry, and complex geometry, revealing insights into their shape and behavior in various dimensions.