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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexJust for completeness and to make links work -- essentially a glorified redirect to _[[submanifold]]_ <a href="https://ncatlab.org/nlab/revision/hypersurface/1">v1</a>, <a href="https://ncatlab.org/nlab/show/hypersurface">current</a>

   Just for completeness and to make links work – essentially a glorified redirect to submanifold

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeSep 4th 2022
   • (edited Sep 4th 2022)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWell, in algebraic geometry a hypersurface is a __codimension 1__ subvariety and there is a number of deep theorems which hold _only_ in that case. Moreover one often restricts to the case given by zeros of a single irreducible polynomial (irreducible hypersurface). I think the codimension 1 qualification is rather standard in modern mathemmatics even in smooth context, unlike in geometrical/topological literature of early part of 20th century when hyper just meant possibly higher dimension.

   Well, in algebraic geometry a hypersurface is a codimension 1 subvariety and there is a number of deep theorems which hold only in that case. Moreover one often restricts to the case given by zeros of a single irreducible polynomial (irreducible hypersurface). I think the codimension 1 qualification is rather standard in modern mathemmatics even in smooth context, unlike in geometrical/topological literature of early part of 20th century when hyper just meant possibly higher dimension.