  We introduce a theory of multigraded Cayley-Chow forms associated to
subvarieties of products of projective spaces. Two new phenomena arise: first,
the construction turns out to require certain inequalities on the dimensions of
projections; and second, in positive characteristic the multigraded Cayley-Chow
forms can have higher multiplicities. The theory also provides a natural
framework for understanding multifocal tensors in computer vision.
