Varieties without extra automorphisms III: hypersurfaces

For any field k and integers n 1, d 3, with (n,d) not equal to (1,3) or (2,4), we exhibit a smooth hypersurface X over k of degree d in Pn+1 such that X has no nontrivial automorphisms over . For (n,d)=(2,4), we find a smooth hypersurface X with the weaker property of having no nontrivial automorphism induced by an automorphism of the ambient Pn+1.