## Kyoto Journal of Mathematics

### Quadratic numerical semigroups and the Koszul property

#### Abstract

Let $H$ be a numerical semigroup. We give effective bounds for the multiplicity $e(H)$ when the associated graded ring $\operatorname{gr}_{\mathfrak{m}}K[H]$ 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

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

Dates
Accepted: 25 April 2016
First available in Project Euclid: 22 April 2017

https://projecteuclid.org/euclid.kjm/1492826434

Digital Object Identifier
doi:10.1215/21562261-2017-0007

Mathematical Reviews number (MathSciNet)
MR3685056

Zentralblatt MATH identifier
06774048

#### Citation

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. https://projecteuclid.org/euclid.kjm/1492826434

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