Abstract
We introduce the concept of homogeneous numerical semigroups and show that all homogeneous numerical semigroups with Cohen–Macaulay tangent cones are of homogeneous type. In embedding dimension three, we classify all numerical semigroups of homogeneous type into numerical semigroups with complete intersection tangent cones and the homogeneous ones which are not symmetric with Cohen–Macaulay tangent cones. We also study the behavior of the homogeneous property by gluing and shiftings to construct large families of homogeneous numerical semigroups with Cohen–Macaulay tangent cones. In particular we show that these properties fulfill asymptotically in the shifting classes. Several explicit examples are provided along the paper to illustrate the property.
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Communicated by Fernando Torres.
Raheleh Jafari was supported in part by a grant from IPM (No. 94130129). Santiago Zarzuela Armengou was supported by MTM2016-7881-P and 2017SGR-585.
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Jafari, R., Zarzuela Armengou, S. Homogeneous numerical semigroups. Semigroup Forum 97, 278–306 (2018). https://doi.org/10.1007/s00233-018-9941-6
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DOI: https://doi.org/10.1007/s00233-018-9941-6