Talk:Intersection number
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Definition
[edit]Intersection number could defined for two manifolds (m and n in m+n) as the degree of some mapping. Just as the de.wikipedia page.--刻意 05:40, 25 December 2008 (UTC)
- How would that improve on the current article? yoyo (talk) 00:40, 10 February 2026 (UTC)
Move?
[edit]Why is this article called "intersection number (algebraic geometry)" rather than "intersection number"? Is it contemplated that there may also be "intersection numbers" in fields other than algebraic geometry? What fields would those be? Should this page be moved to "intersection number"? Michael Hardy (talk) 20:40, 31 December 2008 (UTC)
- The intersection number of a graph, c.f. intersection graph. Akriasas (talk) 19:57, 3 April 2009 (UTC)
"Especially in algebraic geometry" ??? Utter nonsense!
[edit]An early sentence of this article reads as follows:
"In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency."
Intersection number lives in the field of algebraic topology, and is used in any other branch of mathematics where curves, surfaces, and higher dimensional manifolds are studied. But to omit (algebraic) topology from the "especially" clause is utter nonsense.Daqu (talk) 03:38, 30 January 2013 (UTC)
- Why not rewrite the sentence? It's hard to parse, anyway, even for native English speakers. so needs improving.
- How about something like this:
yoyo (talk) 00:37, 10 February 2026 (UTC)"In mathematics, when studying curves, surfaces and higher-dimensional manifolds, especially in such fields as algebraic geometry and algebraic topology, the intersection number generalises the intuitive notion of counting the number of times two curves intersect. Generalisations include to multiple (more than 2) curves, to higher dimensions, and also account properly for tangency."
Intersection multiplicity
[edit]This is a sort of heads-up, but I'm thinking of starting intersection multiplicity by splitting off some materials from this article. I understand two topics are closely related but ultimately distinct and so it is logically clearer to have separate articles. Please express objection if any. -- Taku (talk) 01:25, 10 May 2018 (UTC)
- What is the distinction? Currently, intersection multiplicity redirects to intersection number, which suggests they are identical. yoyo (talk) 00:39, 10 February 2026 (UTC)