Kyoto Journal of Mathematics

Quadratic numerical semigroups and the Koszul property

Jürgen Herzog and Dumitru I. Stamate

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Let H be a numerical semigroup. We give effective bounds for the multiplicity e(H) when the associated graded ring grmK[H] is defined by quadrics. We classify Koszul complete intersection semigroups in terms of gluings. Furthermore, for several classes of numerical semigroups considered in the literature (arithmetic, compound, special almost-complete intersections, 3-semigroups, symmetric or pseudosymmetric 4-semigroups) we classify those which are Koszul.

Article information

Kyoto J. Math., Volume 57, Number 3 (2017), 585-612.

Received: 30 October 2015
Accepted: 25 April 2016
First available in Project Euclid: 22 April 2017

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Zentralblatt MATH identifier

Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
Secondary: 16S37: Quadratic and Koszul algebras 16S36: Ordinary and skew polynomial rings and semigroup rings [See also 20M25] 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)

Koszul ring quadratic ring numerical semigroup tangent cone complete intersection gluing standard basis arithmetic sequence symmetric and pseudosymmetric semigroups


Herzog, Jürgen; Stamate, Dumitru I. Quadratic numerical semigroups and the Koszul property. Kyoto J. Math. 57 (2017), no. 3, 585--612. doi:10.1215/21562261-2017-0007.

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