On Macaulayfication of certain quasi-projective schemes

Abstract

The notion of Macaulayfication, which is analogous of the desingularization, was introduced by Faltings in 1978 and he construct a Macaulayfication of quasi-projective scheme whose non-Cohen-Macaulay locus is of dimension 0 or 1 by a characteristic free method. In this paper, we gave a Macaulayfication of a quasi-projective scheme whose non-Cohen-Macaulay locus is of dimension 2. Of course out method is independent of the characteristic.