## Taiwanese Journal of Mathematics

### Castelnuovo-Mumford Regularity and Hilbert Coefficients of Parameter Ideals

Cao Huy Linh

#### Abstract

Let $A$ be a noetherian local ring of dimension $d \geq 1$ and $\operatorname{depth}(A) \geq d-1$. In this paper, we study the non-positivity for the Hilbert coefficients of parameter ideals in the ring $A$. Moreover, we establish a bound for the Castelnuovo-Mumford regularity of associated graded ring of $A$ with respect to parameter ideal in terms of the first Hilbert coefficient and the dimension.

#### Article information

Source
Taiwanese J. Math., Volume 23, Number 5 (2019), 1115-1131.

Dates
Revised: 15 January 2019
Accepted: 21 January 2019
First available in Project Euclid: 30 January 2019

https://projecteuclid.org/euclid.twjm/1548817227

Digital Object Identifier
doi:10.11650/tjm/190106

Mathematical Reviews number (MathSciNet)
MR4012372

Zentralblatt MATH identifier
07126941

#### Citation

Linh, Cao Huy. Castelnuovo-Mumford Regularity and Hilbert Coefficients of Parameter Ideals. Taiwanese J. Math. 23 (2019), no. 5, 1115--1131. doi:10.11650/tjm/190106. https://projecteuclid.org/euclid.twjm/1548817227

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