  In this paper, we study arithmetic Macaulayfication of projective schemes and
Rees algebras of ideals. We give a necessary and sufficient condition for a
nonsingular projective scheme to have an arithmetic Macaulayfication. If the
scheme is not necessarily nonsingular, we show that our condition give a
sufficient condition for the existence of an arithmetic Macaulayfication. We
also study truncated Rees algebra of an ideal. We show that the truncated Rees
algebra R_\lambda(I) of an ideal I is alway Cohen-Macaulay for \lambda large
enough in some important situations.
