Resultants and the algebraicity of the join pairing on Chow varieties

The Chow/Van der Waerden approach to algebraic cycles via resultants is used to give a purely algebraic proof for the algebraicity of the complex suspension. The algebraicity of the join pairing on Chow varieties then follows. The approach implies a more algebraic proof of Lawson's complex suspension theorem in characteristic 0. The continuity of the action of the linear isometries operad on the group completion of the stable Chow variety is a consequence.