Symmetric powers of complete modules over a two-dimensional regular local ring
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- by Daniel Katz and Vijay Kodiyalam PDF
- Trans. Amer. Math. Soc. 349 (1997), 747-762 Request permission
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.References
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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
- MR Author ID: 321352
- Email: vijay@imsc.ernet.in
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 747-762
- MSC (1991): Primary 13B21, 13B22, 13H05, 13H15
- DOI: https://doi.org/10.1090/S0002-9947-97-01819-9
- MathSciNet review: 1401523