In this article we study the Hilbert function HR of one-dimensional semigroup rings R = k[[S]], with embedding dimension four over an infinite field k. Let S =< e, n2, n3, n4 > and let M = S ?{0}. Consider the Apéry set of S with respect to the multiplicity e and its subsets Ah = {s ? Apéry(S) | s ? hM ? (h + 1)M}, h ≥ 2. Further let D2 ?{n3, n4} be the set of generators with torsion order 1. We prove that HR is non-decreasing at level ≤ 3 and that HR is non decreasing in each of the following cases: if A2 has cardinality ≤ 4, if A3 has cardinality ≤ 3, if A4 = ?, if D2 has cardinality 2, if S has multiplicity ≤ 13.

INdAM meeting: International meeting on numerical semigroups Cortona 2018

Tamone G.
2020-01-01

Abstract

In this article we study the Hilbert function HR of one-dimensional semigroup rings R = k[[S]], with embedding dimension four over an infinite field k. Let S =< e, n2, n3, n4 > and let M = S ?{0}. Consider the Apéry set of S with respect to the multiplicity e and its subsets Ah = {s ? Apéry(S) | s ? hM ? (h + 1)M}, h ≥ 2. Further let D2 ?{n3, n4} be the set of generators with torsion order 1. We prove that HR is non-decreasing at level ≤ 3 and that HR is non decreasing in each of the following cases: if A2 has cardinality ≤ 4, if A3 has cardinality ≤ 3, if A4 = ?, if D2 has cardinality 2, if S has multiplicity ≤ 13.
978-3-030-40821-3
978-3-030-40822-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1034361
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