Variation of Hilbert coefficients
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- by Laura Ghezzi, Shiro Goto, Jooyoun Hong and Wolmer V. Vasconcelos PDF
- Proc. Amer. Math. Soc. 141 (2013), 3037-3048 Request permission
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.References
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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
- MR Author ID: 192104
- 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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3037-3048
- MSC (2010): Primary 13A30; Secondary 13B22, 13H10, 13H15
- DOI: https://doi.org/10.1090/S0002-9939-2013-11774-0
- MathSciNet review: 3068957