Cohen-Macaulay criteria for projective monomial curves via Gröbner bases

DOI10.1007/s40306-018-00302-5zbMath1433.13023arXiv1803.08961OpenAlexW3102547584MaRDI QIDQ2000792

Dumitru Ioan Stamate, Jürgen Herzog

Publication date: 28 June 2019

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.08961

zbMATH Keywords

Gröbner basisarithmetically Cohen-Macaulaynumerical semigroupApéry setprojective monomial curverevlex

Mathematics Subject Classification ID

Commutative semigroups (20M14) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Syzygies, resolutions, complexes and commutative rings (13D02) Semigroup rings, multiplicative semigroups of rings (20M25)

Related Items

Sumsets and projective curves ⋮ Betti sequence of the projective closure of affine monomial curves ⋮ On the associated graded ring of semigroup algebras ⋮ Projective closure of Gorenstein monomial curves and the Cohen-Macaulay property ⋮ The Cohen-Macaulay property of affine semigroup rings in dimension 2 ⋮ Buchsbaumness and Castelnuovo-Mumford regularity of non-smooth monomial curves ⋮ On the fiber cone of monomial ideals ⋮ Algebraic invariants of certain projective monomial curves

Uses Software

• SINGULAR
• Frobby

Cites Work

• On the defining equations of the tangent cone of a numerical semigroup ring
• Periodicity of Betti numbers of monomial curves
• On liaison, arithmetical Buchsbaum curves and monomial curves in \(\mathbb P^3\)
• On monomial curves and Cohen-Macaulay type
• Gröbner-nice pairs of ideals
• Solving thousand-digit Frobenius problems using Gröbner bases
• Generators and relations of abelian semigroups and semigroup rings
• Gluing and Hilbert functions of monomial curves
• Defining ideals of cohen-macaulay semigroup rings
• On Prime Ideals with Generic Zero x i = t n i
• On Cohen-Macaulay subsemigroups of N²
• Defining ideals of Buchsbaum semigroup rings
• Monomial Ideals
• Cohen-Macaulayness of tangent cones
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item