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

 

Symmetric powers of complete modules over a two-dimensional regular local ring


Authors: Daniel Katz and Vijay Kodiyalam
Journal: Trans. Amer. Math. Soc. 349 (1997), 747-762
MSC (1991): Primary 13B21, 13B22, 13H05, 13H15
MathSciNet review: 1401523
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Abstract: Let $(R,m)$ be a two-dimensional regular local ring with infinite residue field. For a finitely generated, torsion-free $R$-module $A$, write $A_{n}$ for the $n$th symmetric power of $A$, mod torsion. We study the modules $A_{n}$, $n \geq 1$, when $A$ is complete (i.e., integrally closed). In particular, we show that $B\cdot A = A_{2}$, for any minimal reduction $B \subseteq A$ and that the ring $\oplus _{n \geq 1} A_{n}$ is Cohen-Macaulay.


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Additional Information

Daniel Katz
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: dlk@math.ukans.edu

Vijay Kodiyalam
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Address at time of publication: Vijay Kodiyalam, Institute of Mathematical Sciences, Tharamani, Madras 600 113, India
Email: vijay@imsc.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01819-9
PII: S 0002-9947(97)01819-9
Received by editor(s): March 28, 1995
Additional Notes: The first author was partially supported by the General Research Fund at the University of Kansas
Article copyright: © Copyright 1997 American Mathematical Society