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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some consequences of $ {\rm dim\,proj}\ \Omega (A)<\infty $

Author: Carol M. Knighten
Journal: Proc. Amer. Math. Soc. 28 (1971), 411-414
MSC: Primary 13.60; Secondary 14.00
MathSciNet review: 0279087
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Abstract: Let $ X$ be an affine variety over a field $ k$ and $ x$ a point on $ X$. We are interested in relating the properties of $ \Omega {(X)_x}$, the Kähler module of differentials of $ x$, with geometric properties of $ X$ at $ x$. Lipman has given necessary and sufficient conditions for $ \Omega {(X)_x}$ to be respectively torsion free and reflexive in the case where $ X$ is locally a complete intersection at $ x$. We give a generalization of these results for the case where the projective dimension (dim proj) of $ \Omega {(X)_x}$ is finite.

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Keywords: Module of differentials, Macaulay ring, projective dimension, torsion free module, reflexive module, nonsingular in codimension $ r$, associated prime ideals
Article copyright: © Copyright 1971 American Mathematical Society