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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On Macaulayfication of Noetherian schemes
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by Takesi Kawasaki PDF
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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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
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2517-2552
  • MSC (1991): Primary 14M05; Secondary 13H10, 14B05, 14E15
  • DOI: https://doi.org/10.1090/S0002-9947-00-02603-9
  • MathSciNet review: 1707481