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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
