  Theorem: If W is a smooth complex projective variety with h^1 (O-script_W) =
0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane
section of a Calabi-Yau variety, unless W is itself a Calabi-Yau.
  Corollary: A smooth hypersurface of degree d in P^n (n >= 2) is a hyperplane
section of a Calabi-Yau variety iff n+2 <= d <= 2n+2.
  The method is to construct out of the variety W a universal family of all
varieties Z for which X is a hyperplane section with normal bundle K_X, and
examine the "bad" singularities of such Z. A motivation is to show many curves
cannot be divisors on a K-3 surface.
