Join (algebraic geometry)

In algebraic geometry, given irreducible subvarieties "V", "W" of a projective space P"n", the ruled join of "V" and "W" is the union of all lines from "V" to "W" in P2"n"+1, where "V", "W" are embedded into P2"n"+1 so that the last (resp. first) "n" + 1 coordinates on "V" (resp. "W") vanish. It is denoted by "J"("V", "W"). For example, if "V" and "W" are linear subspaces, then their join is the linear span of them, the smallest linear subcontaining them.
The join of several subvarieties is defined in a similar way.