nLab hypersurface




Broadly speaking, a “hypersurface” is a higher-dimensional analogue of a surface. Typically the term is used in generalization of curves and surfaces that are embedded into an ambient Cartesian space/Euclidean space – such as is the case for iso-hypersurfaces – and used in this sense the notion is essentially synonymous to that of a submanifold.

In algebraic geometry, a hypersurface is a codimension 1 subvariety.

Last revised on September 4, 2022 at 21:26:56. See the history of this page for a list of all contributions to it.