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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on the non-Cohen-Macaulay locus
of Noetherian schemes


Author: Nguyen Tu Cuong
Journal: Proc. Amer. Math. Soc. 126 (1998), 1017-1022
MSC (1991): Primary 13C99; Secondary 13H10, 14M99
MathSciNet review: 1425118
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Abstract: In this paper we give a notion of polynomial type $p(X)$ of a Noetherian scheme $X$ and define the function $dp:\, X\longrightarrow \mathbb{Z}$ by $dp(x)=\dim O_{X,x} -p(O_{X,x} )$ for all $x\in X.$ Then we show that if $X$ admits a dualizing complex and $X$ is equidimensional, $dp $ is (lower) semicontinuous; moreover, in that case, the non-Cohen-Macaulay locus nCM$(X)=\{ x\in X\mid O_{X,x}$ is not Cohen-Macaulay} is biequidimensional iff $dp $ is constant on nCM$(X).$


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Additional Information

Nguyen Tu Cuong
Affiliation: Institute of Mathematics, P.O. Box 631, BoHo, 10.000 Hanoi, Vietnam
Email: ntcuong@thevinh.ac.vn

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04160-4
PII: S 0002-9939(98)04160-4
Received by editor(s): July 3, 1995
Received by editor(s) in revised form: October 7, 1996
Additional Notes: The author is partially supported by the National Basic Research Program of Vietnam.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society