On Macaulayfication of Noetherian schemes

Kawasaki, Takesi

doi:10.1090/S0002-9947-00-02603-9

On Macaulayfication of Noetherian schemes
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Trans. Amer. Math. Soc. 352 (2000), 2517-2552 Request permission

Abstract:

The Macaulayfication of a Noetherian scheme $X$ is a birational proper morphism from a Cohen-Macaulay scheme to $X$. In 1978 Faltings gave a Macaulayfication of a quasi-projective scheme if its non-Cohen-Macaulay locus is of dimension $0$ or $1$. In the present article, we construct a Macaulayfication of Noetherian schemes without any assumption on the non-Cohen-Macaulay locus. Of course, a desingularization is a Macaulayfication and, in 1964, Hironaka already gave a desingularization of an algebraic variety over a field of characteristic $0$. Our method, however, to construct a Macaulayfication is independent of the characteristic.

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