On Macaulayfication of Certain Quasi-projective Schemes
نویسندگان
چکیده
The Macaulayfication of a Noetherian scheme X is a birational proper morphism Y → X such that Y is a CohenMacaulay scheme. Of course, a desingularization is a Macaulayfication and Hironaka gave a desingularization of arbitrary algebraic variety over a field of characteristic 0. In 1978 Faltings gave a Macaulayfication of a quasi-projective scheme whose nonCohen-Macaulay locus is of dimension 0 or 1 by a characteristic-free method. In the present article, we shall construct a Macaulayfication of a quasi-projective scheme if the dimension of its non-CohenMacaulay locus is at most 2. Of course, our method is independent of the characteristic of a scheme.
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