Talk:Complete intersection

That part on wiles proof needs to be adjusted, just the fact that Hecke algebra is a complete intersection is not the entire story of the proof —Preceding unsigned comment added by 129.175.50.230 (talk) 16:35, 12 December 2009 (UTC)

The section on this page about the twisted cubic does not seem to be fully in agreement with the wiki page on twisted cubics. On that page, it says that the twisted cube can indeed be cut out using just two polynomials, and thus is a set-theoretic complete intersection. It explains, that the twisted cubed is not, though, an ideal-theoretic complete intesection. Sjg sjg (talk) 18:01, 17 November 2010 (UTC)

This article defines a set theoretic complete intersection. It should have said in addition that the codimension number of polynomials (in the article) generate the ideal of the variety (that is the full ideal of polynomials that vanish on it). The article is misleading and should be redone or removed. (See Hartshorne, Algebraic Geometry, Springer GTM, 1977, p.14 2.17) — Preceding unsigned comment added by 76.88.17.106 (talk) 17:24, 19 August 2011 (UTC)

Why does the page only describe complete intersections in projective space? The article should be rewritten. — Preceding unsigned comment added by 142.1.102.126 (talk) 15:19, 26 March 2012 (UTC)

Clarification in definition of variety.

Does "affine set" as referenced in the definition of this page defined with respect to irreducible algebraic sets? Or are we using the term "variety" to more loosely refer to algebraic sets which may or may not be irreducible? J.G.131 (talk) 19:56, 8 June 2026 (UTC)