L2-Betti Numbers of Hypersurface Complements

In [2], it was shown that if A is an affine hyperplane arrangement in C-n, then at most one of the L-2-Betti numbers b(i)((2))(C-n \ A, id) is nonzero. In this note, we prove an analogous statement for complements of complex affine hypersurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of [6, 9] about L-2-Betti numbers of plane curve complements.