Taiwanese Journal of Mathematics

Castelnuovo-Mumford Regularity and Hilbert Coefficients of Parameter Ideals

Cao Huy Linh

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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.

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Taiwanese J. Math., Advance publication (2019), 17 pages.

First available in Project Euclid: 30 January 2019

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Primary: 13D45: Local cohomology [See also 14B15] 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 14B15: Local cohomology [See also 13D45, 32C36]

Hilbert coefficients the depth of associated graded rings parameter ideals Castelnuovo-Mumford regularity postulation number


Linh, Cao Huy. Castelnuovo-Mumford Regularity and Hilbert Coefficients of Parameter Ideals. Taiwanese J. Math., advance publication, 30 January 2019. doi:10.11650/tjm/190106. https://projecteuclid.org/euclid.twjm/1548817227

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