Transactions of the American Mathematical Society

Author(s): Takesi Kawasaki
Journal: Trans. Amer. Math. Soc. 352 (2000), 2517-2552.
MSC (1991): Primary 14M05; Secondary 13H10, 14B05, 14E15
Posted: February 29, 2000
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The Macaulayfication of a Noetherian scheme

is a birational proper morphism from a Cohen-Macaulay scheme to

. In 1978 Faltings gave a Macaulayfication of a quasi-projective scheme if its non-Cohen-Macaulay locus is of dimension

. 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

. Our method, however, to construct a Macaulayfication is independent of the characteristic.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 14M05, 13H10, 14B05, 14E15

Takesi Kawasaki
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Hachioji-shi Minami-Ohsawa 1-1, Tokyo 192-0397, Japan
Email: kawasaki@comp.metro-u.ac.jp

DOI: 10.1090/S0002-9947-00-02603-9
PII: S 0002-9947(00)02603-9
Keywords: Blowing-up, Cohen-Macaulay scheme, desingularization, dualizing complex, Macaulayfication
Received by editor(s): November 11, 1996
Posted: February 29, 2000
Additional Notes: The author is supported by Grant-in-Aid for Co-Operative Research.
Copyright of article: Copyright 2000, American Mathematical Society

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