Complete-intersection realization conjecture for toric varieties

A toric variety is an algebraic variety equipped with the torus action arising from a toric construction; a Calabi–Yau hypersurface is a hypersurface with trivial canonical class. Complete-intersection realization conjecture. All toric varieties, and hence their Calabi–Yau hypersurfaces, can be realized as suitably chosen, possibly generalized, complete intersections in products of projective spaces. The claim is described as a sweeping extrapolation and is far from obvious; no resolution is supplied here.