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Resurgence and Castelnuovo-Mumford regularity of certain monomial curves in \(\mathbb{A}^3\). (English) Zbl 1472.13008

Author’s abstract: Let \(p\) be the defining ideal of the monomial curve \(\mathcal{C}(2q +1, 2q +1+m, 2q +1+2m)\) in the affine space \(\mathbb{A}^3_k\) parameterised by \((x^{2q+1}, x^{2q+1+m}, x^{2q+1+2m})\), where \(gcd(2q + 1, m) =1\). In this paper we compute the resurgence of \(p\), the Waldschmidt constant of \(p\) and the Castelnuovo-Mumford regularity of the symbolic powers of \(p\).

MSC:

13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13H05 Regular local rings
13H15 Multiplicity theory and related topics
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
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References:

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