On the Apéry sets of monomial curves

In this paper, we use the Apéry table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Apéry table of a numerical semigroup of embedding dimension 3, when th...

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Autores: Cortadellas Benítez, Teresa, Jafari, Raheleh, Zarzuela, Santiago
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/194824
Acceso en línea:https://hdl.handle.net/2445/194824
Access Level:acceso abierto
Palabra clave:Anells commutatius
Anells locals
Àlgebra commutativa
Commutative rings
Local rings
Commutative algebra
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spelling On the Apéry sets of monomial curvesCortadellas Benítez, TeresaJafari, RahelehZarzuela, SantiagoAnells commutatiusAnells localsÀlgebra commutativaCommutative ringsLocal ringsCommutative algebraIn this paper, we use the Apéry table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Apéry table of a numerical semigroup of embedding dimension 3, when the tangent cone of its monomial curve is Buchsbaum or 2-Buchsbaum, and give new proofs for two conjectures raised by Sapko (Commun. Algebra 29:4759-4773, 2001) and Shen (Commun. Algebra 39:1922-1940, 2001). We also provide a new simple proof in the case of monomial curves for Sally's conjecture (Numbers of Generators of Ideals in Local Rings, 1978) that the Hilbert function of a one-dimensional Cohen-Macaulay ring with embedding dimension three is non-decreasing. Finally, we obtain that monomial curves of embedding dimension 4 whose tangent cones are Buchsbaum, and also monomial curves of any embedding dimensions whose numerical semigroups are balanced, have non-decreasing Hilbert functions. Numerous examples are provided to illustrate the results, most of them computed by using the NumericalSgps package of GAP (Delgado et al., NumericalSgps-a GAP package, 2006).Springer Verlag2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/194824Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1007/s00233-012-9445-8Semigroup Forum, 2012, vol. 86, num. 2, p. 289-320https://doi.org/10.1007/s00233-012-9445-8(c) Springer Verlag, 2012info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1948242026-05-27T06:46:51Z
dc.title.none.fl_str_mv On the Apéry sets of monomial curves
title On the Apéry sets of monomial curves
spellingShingle On the Apéry sets of monomial curves
Cortadellas Benítez, Teresa
Anells commutatius
Anells locals
Àlgebra commutativa
Commutative rings
Local rings
Commutative algebra
title_short On the Apéry sets of monomial curves
title_full On the Apéry sets of monomial curves
title_fullStr On the Apéry sets of monomial curves
title_full_unstemmed On the Apéry sets of monomial curves
title_sort On the Apéry sets of monomial curves
dc.creator.none.fl_str_mv Cortadellas Benítez, Teresa
Jafari, Raheleh
Zarzuela, Santiago
author Cortadellas Benítez, Teresa
author_facet Cortadellas Benítez, Teresa
Jafari, Raheleh
Zarzuela, Santiago
author_role author
author2 Jafari, Raheleh
Zarzuela, Santiago
author2_role author
author
dc.subject.none.fl_str_mv Anells commutatius
Anells locals
Àlgebra commutativa
Commutative rings
Local rings
Commutative algebra
topic Anells commutatius
Anells locals
Àlgebra commutativa
Commutative rings
Local rings
Commutative algebra
description In this paper, we use the Apéry table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Apéry table of a numerical semigroup of embedding dimension 3, when the tangent cone of its monomial curve is Buchsbaum or 2-Buchsbaum, and give new proofs for two conjectures raised by Sapko (Commun. Algebra 29:4759-4773, 2001) and Shen (Commun. Algebra 39:1922-1940, 2001). We also provide a new simple proof in the case of monomial curves for Sally's conjecture (Numbers of Generators of Ideals in Local Rings, 1978) that the Hilbert function of a one-dimensional Cohen-Macaulay ring with embedding dimension three is non-decreasing. Finally, we obtain that monomial curves of embedding dimension 4 whose tangent cones are Buchsbaum, and also monomial curves of any embedding dimensions whose numerical semigroups are balanced, have non-decreasing Hilbert functions. Numerous examples are provided to illustrate the results, most of them computed by using the NumericalSgps package of GAP (Delgado et al., NumericalSgps-a GAP package, 2006).
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/194824
url https://hdl.handle.net/2445/194824
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1007/s00233-012-9445-8
Semigroup Forum, 2012, vol. 86, num. 2, p. 289-320
https://doi.org/10.1007/s00233-012-9445-8
dc.rights.none.fl_str_mv (c) Springer Verlag, 2012
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Verlag, 2012
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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