FWIW, Joe Harris (in the cited ref) claims that the Segre embedding is the categorical product for projective varieties; the book however, brushes only very lightly on category theory. linas 14:19, 18 December 2006 (UTC)
- The categorical product of Pm and Pn is Pm×Pn (defined as a fiber product if you want) in any reasonable category of algebraic varieties over a fixed field. The categorical point about Segre is that it gives the easy proof that the subcategory of projective varieties contains Pm×Pn. If you like, the issue is not what the product is, but where it is. The Segre embedding is strictly a morphism, not an object. Charles Matthews 16:05, 18 December 2006 (UTC)
So, which is it? Embedding or Mapping?
The title of this article is Segre embedding. This name is nowhere to be found in the Definition section. Apparently a Segre Mapping is identical to an Segre Embedding, but this is not self-evident and, like ANY terminology, should be made explicit. I would add an "also known as" sentence to the lede, if I were doing more than speculating on this identity. Also, would it be too much to ask that one of the "examples" be reduced to an actual numerical case? I have no idea what is meant by "zero locus", nor why the |2x2 complex| determinant defines the 1x1 example: 2*2-1 = 3, so how does a determinant, dependent on 4 scalars, apply? (As far as I can see, the four scalars are all members of C¹ (or R²) (by definition if you use them to compute the determinant, right?). I also am not familiar with the X1:X2:X3 notation; how does that differ from the common X1,X2,X3 notation? This seems to be one of the all too common instances of articles which if you can understand them, then you don't need them. — Preceding unsigned comment added by 18.104.22.168 (talk) 10:06, 15 June 2014 (UTC)