A singular point of an algebraic variety is a point where the variety is not well-behaved in terms of its geometric structure. More formally, a point \( P \) on an algebraic variety \( V \) defined by a set of polynomial equations is termed a singular point if the local behavior of the variety at that point exhibits some form of "singularity," meaning that it fails to meet certain smoothness conditions.
Articles by others on the same topic
A point of an irreducible variety is singular when . Equivalently, its local ring is not regular. The singular locus is the complement of the smooth locus.