  We prove a global nonlinear Brascamp-Lieb inequality for a general class of
maps, encompassing polynomial and rational maps, as a consequence of the
multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate
a natural affine-invariant weight that compensates for local degeneracies, and
yields a uniform constant that depends only on the 'degree' of the maps
involved.
