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Applicant:
Indian Institute of Technology (IIT) Patna 
Author:
K. Saloni, Anupam Saikia, , 
Corresponding Authors:
Anupam Saikia 
DOI #:
https://doi.org/10.1016/j.jalgebra.2017.12.022 
Title:
Bounding Hilbert coefficients of parameter ideals 
Journal:
J. Algebra 
Year:
2018 
Volume:
501 
Page:
328-344 
Keywords:
Hilbert–Samuel polynomial, Hilbert coefficients, Local cohomology module 
Abstract:
Let (R, m) be a Noetherian local ring of dimension d > 0 and depth R ≥ d − 1. Let Q be a parameter ideal of R. In this paper, we derive uniform lower and upper bounds for the Hilbert coefficient ei(Q) under certain assumptions on the depth of associated graded ring G(Q). For 2 ≤ i ≤ d, we show that (1) ei(Q) ≤ 0 provided depth G(Q) ≥ d − 2 and (2) ei(Q) ≥ −λR(Hd−1 m (R)) provided depth G(Q) ≥ d − 1. It is proved that e3(Q) ≤ 0. Further, we obtain a necessary condition for the vanishing of the last coefficient ed(Q). As a consequence, we characterize the vanishing of e2(Q). Our results generalize [5, Theorem 3.2] and [11, Corollary 4.5]. 
Entered by:
Venkata Dantham on 2020-08-04 
 
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