Journal of Commutative Algebra

Castelnuovo-Mumford regularity of symbolic powers of two-dimensional square-free monomial ideals

Le Tuan Hoa and Tran Nam Trung

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Let $I$ be a square-free monomial ideal of a polynomial ring $R$ such that $\dim (R/I) = 2$. We give explicit formulas for computing the $a_i$-invariants $a_i(R/I^{(n)})$, $i=1,2$, and the Castelnuovo-Mumford regularity $\reg (R/I^{(n)})$ for all $n$. The values of these functions depend on the structure of an associated graph. It turns out that these functions are linear functions of $n$ for all $n \ge 2$.

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J. Commut. Algebra, Volume 8, Number 1 (2016), 77-88.

First available in Project Euclid: 28 March 2016

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Zentralblatt MATH identifier

Primary: 13D45: Local cohomology [See also 14B15]

Castelnuovo-Mumford regularity symbolic power square-free monomial ideals


Hoa, Le Tuan; Trung, Tran Nam. Castelnuovo-Mumford regularity of symbolic powers of two-dimensional square-free monomial ideals. J. Commut. Algebra 8 (2016), no. 1, 77--88. doi:10.1216/JCA-2016-8-1-77.

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