Homogeneous numerical semigroups

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 in to numerical semigroups with complete intersection tangent cones and the homogeneous ones with Cohen-Macaulay tangent cones. We also study the behavior of the homogeneous property by gluing and shiftings to construct a large family of homogeneous numerical semigroups with Cohen-Macaulay tangent cones. In particular we show that these properties fulfill assymptotically in the shifting classes. Several explicit examples are provided along the paper to illustrate the property.

final version; published online in Semigroup Forum (https://doi.org/10.1007/s00233-018-9941-6)

References in corpus (1)

• numericalsgps, a GAP package for numerical semigroups

Cited by in corpus (6)

• Betti numbers for numerical semigroup rings
• Betti numbers for certain Cohen-Macaulay tangent cones
• Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups
• The Betti Numbers of Kunz-Waldi Semigroups
• Proyective Cohen-Macaulay monomial curves and their affine charts
• Minimal free resolution of generalized repunit algebras