Join (algebraic geometry)
In algebraic geometry, given irreducible subvarieties V, W of a projective space Pn, the ruled join of V and W is the union of all lines from V to W in P2n+1, where V, W are embedded into P2n+1 so that the last n + 1 coordinates on V vanish. It is denoted by J. 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.
