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| Paper IPM / M / 15189 |
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| Abstract: | |
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We introduce the concept of homogeneous numerical semigrou
ps and
show that all homogeneous numerical semigroups with Cohen-
Macaulay tangent cones
are of homogeneous type. In embedding dimension three, we cl
assify all numerical
semigroups of homogeneous type into numerical semigroups w
ith complete intersec-
tion tangent cones and the homogeneous ones which are not sym
metric with Cohen-
Macaulay tangent cones. We also study the behavior of the hom
ogeneous property by
gluing and shiftings to construct large families of homogen
eous numerical semigroups
with Cohen-Macaulay tangent cones. In particular we show th
at these properties
fulfill asymptotically in the shifting classes. Several exp
licit examples are provided
along the paper to illustrate the property.
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