Talk:Projective cone

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Some point I'd like to discuss here :

I don't agree with apex. Not only is that completely new to me, apex seems to be more a specific point on top of a three dimensional object, something sharp. Top is more conventional? Evilbu 16:17, 14 February 2006 (UTC)Reply

Sorry, my fault. I suppose that "top" is OK, although it seems just as strange. (Since the lines continue beyond it, R is never the "top" of the object!) Jorge Stolfi 23:45, 14 February 2006 (UTC)Reply

I'm very new to wikipedia, so my first paragraph can be improper yes. However, then where should my remark about the singularities be? Evilbu 16:17, 14 February 2006 (UTC)Reply

That remark could be added after the current last paragraph. However, note that the article must make some sense to the reader who gets here directly. So, if that remark refers to some complicated application of the concept, that cannot be explained in a sentence or two, perhaps it you should put the remark in the page of that application, not here. Jorge Stolfi 23:58, 14 February 2006 (UTC)Reply

Why did you remove the \pi_{r} It is a notation we use at university. Why is R better? It is not that important however. Evilbu 16:17, 14 February 2006 (UTC)Reply

For one thing, one should use the simplest notation that is sufficient for the purpose at hand. Moreover, that kind of notation (where the subscript indicates the dimension) is inappropriate because, to most readers, it means the element of index r in a collection called π. In particular, it also implies that π_r = π_s whenever r = s. That obviously is not the intended meaning. Jorge Stolfi 23:58, 14 February 2006 (UTC)Reply

When R is empty, I think the best thing is not to define a cone. Conventions might differ but that is what I saw. Evilbu 16:17, 14 February 2006 (UTC)Reply

Your remark about where the name cone comes from is good, but shouldn't you add that you a working in three d? Evilbu 16:17, 14 February 2006 (UTC)Reply

That does not seem necessary, since the dimension of X has to be at least three for R and S to be disjoint, and higher dimensions do not hurt --- the cones will all be projectively equivalent. Jorge Stolfi 23:58, 14 February 2006 (UTC)Reply