mathematical singularity
in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability
regular singular point
concept in differential equation mathematics
ring singularity
Ring-shaped gravitational singularity of a rotating blackhole
gravitational singularity
location in space-time where the gravitational field of a celestial body becomes infinite
singular point of an algebraic variety
point of an algebraic variety without a defined tangent space