Ruled join

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 (resp. first) n + 1 coordinates on V (resp. W) vanish.^[1] 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.

See also

• Secant variety