We compare the cohomological annihilators of a projective subscheme and its
general hypersurface section. We show that we can conclude from the k-Buch
sbaumness of the hypersurface section to that of the original scheme if the
hypersurface has degree at least k + 1. We describe examples which show th
at this result is best possible. (C) 2000 Elsevier Science B.V. All rights
reserved.