Ruled join

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Short description: Concept in mathematics

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

References

  1. Fulton 1998, Example 8.4.5.