On the defining equations of the tangent cone of a numerical semigroup ring

DOI10.1016/j.jalgebra.2014.07.008zbMath1333.13023arXiv1308.4644OpenAlexW2045824603MaRDI QIDQ406344

Jürgen Herzog, Dumitru Ioan Stamate

Publication date: 8 September 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4644

zbMATH Keywords

number of generatorsBetti numberstangent conesbinomial idealsnumerical semigroup ringsshifted sequenceswidth of a numerical semigroup

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Syzygies, resolutions, complexes and commutative rings (13D02) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Other special types of modules and ideals in commutative rings (13C13)

Related Items (19)

On the Hilbert series of the tangent cones for some 4-generated pseudosymmetric monomial curves ⋮ Syzygies of \textit{GS} monomial curves and Weierstrass property ⋮ On intersections of complete intersection ideals ⋮ Asymptotic properties in the shifted family of a numerical semigroup with few generators ⋮ On pseudo symmetric monomial curves ⋮ Affine monomial curves ⋮ On the Betti numbers of the tangent cones for Gorenstein monomial curves ⋮ 4-generated pseudo symmetric monomial curves with not Cohen–Macaulay tangent cones ⋮ Structure of Semigroup Rings (Survey) ⋮ On parametrized families of numerical semigroups ⋮ Homogeneous numerical semigroups ⋮ Canonical trace ideal and residue for numerical semigroup rings ⋮ On minimal presentations of shifted affine semigroups with few generators ⋮ BETTI NUMBERS FOR CERTAIN COHEN–MACAULAY TANGENT CONES ⋮ Cohen-Macaulay criteria for projective monomial curves via Gröbner bases ⋮ LIFTINGS OF A MONOMIAL CURVE ⋮ On the Cohen–Macaulayness of tangent cones of monomial curves inA4(K) ⋮ Betti numbers of Bresinsky’s curves in 𝔸4 ⋮ The generators, relations and type of the Backelin semigroup

Uses Software

• CoCoA
• SINGULAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Good embedding dimensions for Gorenstein singularities
• Minimal sets of generators for the relation ideals of certain monomial curves
• The leading ideal of a complete intersection of height two. II.
• Minimal free resolution of the associated graded ring of monomial curves of generalized arithmetic sequences
• Minimal graded free resolutions for monomial curves defined by arithmetic sequences
• Generators and relations of abelian semigroups and semigroup rings
• Minimal free resolutions for certain affine monomial curve
• When is a regular sequence super regular?
• On Prime Ideals with Generic Zero x i = t n i
• Cohen-Macaulayness of tangent cones
• The Value-Semigroup of a One-Dimensional Gorenstein Ring

This page was built for publication: On the defining equations of the tangent cone of a numerical semigroup ring