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

 

Variation of Hilbert coefficients


Authors: Laura Ghezzi, Shiro Goto, Jooyoun Hong and Wolmer V. Vasconcelos
Journal: Proc. Amer. Math. Soc. 141 (2013), 3037-3048
MSC (2010): Primary 13A30; Secondary 13B22, 13H10, 13H15
Published electronically: June 3, 2013
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Abstract: For a Noetherian local ring $ (\mathbf {R}, \mathfrak{m})$, the first two Hilbert coefficients, $ e_0$ and $ e_1$, of the $ I$-adic filtration of an $ \mathfrak{m}$-primary ideal $ I$ are known to code for properties of $ \mathbf {R}$, of the blowup of $ \operatorname {Spec}(\mathbf {R})$ along $ V(I)$, and even of their normalizations. We give estimations for these coefficients when $ I$ is enlarged (in the case of $ e_1$ in the same integral closure class) for general Noetherian local rings.


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Additional Information

Laura Ghezzi
Affiliation: Department of Mathematics, New York City College of Technology-CUNY, 300 Jay Street, Brooklyn, New York 11201
Email: lghezzi@citytech.cuny.edu

Shiro Goto
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan
Email: goto@math.meiji.ac.jp

Jooyoun Hong
Affiliation: Department of Mathematics, Southern Connecticut State University, 501 Crescent Street, New Haven, Connecticut 06515-1533
Email: hongj2@southernct.edu

Wolmer V. Vasconcelos
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email: vasconce@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11774-0
PII: S 0002-9939(2013)11774-0
Received by editor(s): August 22, 2011
Received by editor(s) in revised form: December 3, 2011
Published electronically: June 3, 2013
Additional Notes: The first author was partially supported by a grant from the City University of New York PSC-CUNY Research Award Program-41
The second author was partially supported by Grant-in-Aid for Scientific Researches (C) in Japan (19540054) and by a grant from MIMS (Meiji Institute for Advanced Study of Mathematical Sciences)
The fourth author was partially supported by the NSF
Communicated by: Irena Peeva
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.