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Bounds on the normal Hilbert coefficients


Authors: Alberto Corso, Claudia Polini and Maria Evelina Rossi
Journal: Proc. Amer. Math. Soc. 144 (2016), 1919-1930
MSC (2010): Primary 13A30, 13B21, 13D40; Secondary 13H10, 13H15
DOI: https://doi.org/10.1090/proc/12858
Published electronically: October 1, 2015
MathSciNet review: 3460155
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Abstract: In this paper we consider extremal and almost extremal bounds on the normal Hilbert coefficients of $ {\mathfrak{m}}$-primary ideals of an analytically unramified Cohen-Macaulay ring $ R$ of dimension $ d>0$ and infinite residue field. In these circumstances we show that the associated graded ring of the normal filtration of the ideal is either Cohen-Macaulay or almost Cohen-Macaulay.


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Additional Information

Alberto Corso
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: alberto.corso@uky.edu

Claudia Polini
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: cpolini@nd.edu

Maria Evelina Rossi
Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16132 Genova, Italy
Email: rossim@dima.unige.it

DOI: https://doi.org/10.1090/proc/12858
Keywords: Hilbert functions, Hilbert coefficients, associated graded rings, Sally modules, normal filtrations
Received by editor(s): October 15, 2014
Received by editor(s) in revised form: June 8, 2015
Published electronically: October 1, 2015
Additional Notes: The second author was partially supported by NSF grant DMS-1202685 and NSA grant H98230-12-1-0242.
The third author was partially supported by MIUR grant PRIN-GVS
Communicated by: Irena Peeva
Article copyright: © Copyright 2015 American Mathematical Society