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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Macaulayfication of Noetherian schemes


Author: Takesi Kawasaki
Journal: Trans. Amer. Math. Soc. 352 (2000), 2517-2552
MSC (1991): Primary 14M05; Secondary 13H10, 14B05, 14E15
Published electronically: February 29, 2000
MathSciNet review: 1707481
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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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Additional Information

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: http://dx.doi.org/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
Published electronically: February 29, 2000
Additional Notes: The author is supported by Grant-in-Aid for Co-Operative Research.
Article copyright: © Copyright 2000 American Mathematical Society