Let X be a smooth aane variety of dimension n > 2. Assume that the group H 1 (X; Z) is a torsion group and that (X) = 1. Let Y be a projectively smooth aane hypersurface Y C n+1 of degree d > 1, which is smooth at innnity. Then there is no injective polynomial mapping f : X ! Y: This contradicts a result of Peretz 5].