## Journal of Commutative Algebra

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

#### Abstract

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 $n \ge 2$.

#### Article information

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

Dates
First available in Project Euclid: 28 March 2016

https://projecteuclid.org/euclid.jca/1459169546

Digital Object Identifier
doi:10.1216/JCA-2016-8-1-77

Mathematical Reviews number (MathSciNet)
MR3482347

Zentralblatt MATH identifier
06561092

Subjects

#### Citation

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. https://projecteuclid.org/euclid.jca/1459169546

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