On some conjectures about the Chern numbers of filtrations

Mandal, Mousumi ; Singh, Balwant ; Verma, J. K. (2011) On some conjectures about the Chern numbers of filtrations Journal of Algebra, 325 (1). pp. 147-162. ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jalgebra.2010.10.008

Abstract

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e1(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 {I̅n} 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Chern Number; Hilbert Polynomial; Cohen-Macaulay Ring; Face Ring; Filtration of Ideals
ID Code:53474
Deposited On:10 Aug 2011 09:53
Last Modified:18 May 2016 06:35

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