  We construct complex projective schemes with Lyubeznik numbers of their cones
depending on the choices of projective embeddings. This answers a question of
G. Lyubeznik in the characteristic 0 case. It contrasts with a theorem of W.
Zhang in the positive characteristic case where the Frobenius endomorphism is
used. Reducibility of schemes is essential in our argument. B. Wang recently
constructed examples of irreducible projective schemes (which are not normal)
from our examples of reducible ones. So the question is still open in the
normal singular case.
