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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/3379

Title: On some conjectures about the Chern numbers of filtrations
Authors: MANDAL, M
SINGH, B
VERMA, JK
Keywords: hilbert coefficients
graded rings
local-rings
Issue Date: 2010
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: JOURNAL OF ALGEBRA, 325(1), 147-162
Abstract: Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(A) of the Hilbert polynomial of an I-admissible filtration A is called the Chern number of A. The Positivity Conjecture of Vasconcelos for the Chern number of the integral closure filtration {(I(n)) over bar} is proved for a 2-dimensional complete local domain and more generally for any analytically unramified local ring R whose integral closure in its total ring of fractions is Cohen-Macaulay as an R-module. It is proved that if I is a parameter ideal then the Chern number of the I-adic filtration is non-negative. Several other results on the Chern number of the integral closure filtration are established, especially in the case when R is not necessarily Cohen-Macaulay.
URI: http://dx.doi.org/10.1016/j.jalgebra.2010.10.008
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3379
http://hdl.handle.net/10054/3379
ISSN: 0021-8693
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