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On some conjectures about the Chern numbers of filtrations

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Title On some conjectures about the Chern numbers of filtrations
 
Creator MANDAL, M
SINGH, B
VERMA, JK
 
Subject hilbert coefficients
graded rings
local-rings
chern number
hilbert polynomial
cohen-macaulay ring
face ring
filtration of ideals
 
Description 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.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2011-07-12T16:23:51Z
2011-12-26T12:48:58Z
2011-12-27T05:34:32Z
2011-07-12T16:23:51Z
2011-12-26T12:48:58Z
2011-12-27T05:34:32Z
2010
 
Type Article
 
Identifier JOURNAL OF ALGEBRA, 325(1), 147-162
0021-8693
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
 
Language en