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

 

Bounding the first Hilbert coefficient


Authors: Krishna Hanumanthu and Craig Huneke
Journal: Proc. Amer. Math. Soc. 140 (2012), 109-117
MSC (2010): Primary 13A30, 13B22, 13D40, 13H15
Published electronically: May 20, 2011
MathSciNet review: 2833522
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Abstract: This paper gives new bounds on the first Hilbert coefficient of an ideal of finite colength in a Cohen-Macaulay local ring. The bound given is quadratic in the multiplicity of the ideal. We compare our bound to previously known bounds and give examples to show that at least in some cases it is sharp. The techniques come largely from work of Elias, Rossi, Valla, and Vasconcelos.


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Additional Information

Krishna Hanumanthu
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: khanuma@math.ku.edu

Craig Huneke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: huneke@math.ku.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11021-9
PII: S 0002-9939(2011)11021-9
Received by editor(s): November 10, 2010
Published electronically: May 20, 2011
Additional Notes: The first author was partially supported by Robert D. Adams Visiting Assistant Professorship Fund.
The second author was partially supported by the National Science Foundation, grant DMS-0756853
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.