Affine monomial curves

DOI10.1007/s12044-022-00670-xzbMath1487.14073arXiv2008.00246OpenAlexW4281656230MaRDI QIDQ2672054

Indranath Sengupta

Publication date: 8 June 2022

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.00246

zbMATH Keywords

Gröbner basissyzygiescomplete intersectionnumerical semigroupsBetti numbersFrobenius numbermonomial curvesApéry setsymmetric numerical semigroupsminimal presentationblowup algebrasset theoretic complete intersectionderivation moduleFrancia's conjecture

Mathematics Subject Classification ID

Commutative semigroups (20M14) Plane and space curves (14H50) Computational aspects of algebraic curves (14Q05)

Uses Software

• GAP
• Macaulay2
• SINGULAR

Cites Work

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• On the defining equations of the tangent cone of a numerical semigroup ring
• Graded syzygies
• On the smoothness of blowups for certain monomial curves
• Generators for the derivation modules and the relation ideals of certain curves
• Certain monomial curves are set-theoretic complete intersections
• Hilbert functions and symbolic powers
• On the finite generation of symbolic blow-ups
• Symmetric semigroups of integers generated by 4 elements
• Affine curves in characteristic p are set theoretic complete intersections
• The Zariski-Lipman conjecture in the graded case
• Monomial Gorenstein curves in \(A^4\) as set-theoretic complete intersections
• Minimal sets of generators for the relation ideals of certain monomial curves
• Betti numbers for numerical semigroup rings
• On the set-theoretic complete intersection problem for monomial curves in \(\mathbb{A}^ n\) and \(\mathbb{P}^ n\)
• Computing in algebraic geometry. A quick start using SINGULAR
• Minimal graded free resolutions for monomial curves defined by arithmetic sequences
• The monomial curves associated with balanced semigroups are set-theoretic complete intersections
• Generators and relations of abelian semigroups and semigroup rings
• Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension
• Minimal graded free resolutions for monomial curves in 𝔸⁴defined by almost arithmetic sequences
• Minimal free resolutions for certain affine monomial curve
• On finite generation of symbolic algebras of monomial primes
• Singularity of Monomial Curves in A³ and Gorenstein Monomial Curves in A⁴
• On set-theoretic complete intersections in the projective space
• On Prime Ideals with Generic Zero x i = t n i
• Monomial Space Curves in A 3 as Set-Theoretic Complete Intersections
• The herzog-vasconcelos conjecture for affine semigroup rings
• On the smoothness of blow ups
• A Minimal Free Resolution for Certain Monomial Curves in 𝔸⁴
• Minimal set of generators for the derivation module of certain monomial curves
• A Gröbner Basis for Certain Affine Monomial Curves
• Numerical semigroups generated by concatenation of arithmetic sequences
• Betti numbers of Bresinsky’s curves in 𝔸4
• The Rees Algebra for Certain Monomial Curves
• Symbolic algebras of monomial primes.
• Monomial Gorenstein ideals
• Normal blow-ups and their expected defining equations

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