Standard bases for local rings of branches and their modules of differentials

DOI10.1016/j.jsc.2006.02.008zbMath1121.14048OpenAlexW2030301892MaRDI QIDQ2457416

Marcelo Escudeiro Hernandes, Abramo Hefez

Publication date: 23 October 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2006.02.008

zbMATH Keywords

Kähler differentialsnumerical invariantsstandard basescurve singularitiessemigroups of values

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Derivations and commutative rings (13N15) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Computational aspects of algebraic curves (14Q05) Singularities of curves, local rings (14H20)

Related Items (18)

Simple singularities of reducible curves in characteristicp > 0 ⋮ On the values of logarithmic residues along curves ⋮ Simple singularities of parametrized plane curves in positive characteristic ⋮ On the analytic invariants and semiroots of plane branches ⋮ Analytic semiroots for plane branches and singular foliations ⋮ Characterization of uni-modal parametric plane curve singularities ⋮ The value semiring of an algebroid curve ⋮ Standard bases for local rings of branches and their modules of differentials ⋮ Irreducibility criterion for algebroid curves ⋮ An algorithm for computing torsion differential forms associated with an isolated hypersurface singularity ⋮ Moduli spaces for topologically quasi-homogeneous functions ⋮ Standard bases for fractional ideals of the local ring of an algebroid curve ⋮ Analytic classification of plane branches up to multiplicity 4 ⋮ On Polars of Plane Branches ⋮ Canonical bases of modules over one dimensional \(\mathbf{K}\)-algebras ⋮ Symmetry of maximals for fractional ideals of curves ⋮ On the value set of 1-forms for plane branches ⋮ The Analytic Classification of Irreducible Plane Curve Singularities

Cites Work

• Standard bases and some computations in rings of power series
• Efficient solution of linear diophantine equations
• The Milnor number and deformations of complex curve singularities
• An efficient incremental algorithm for solving systems of linear diophantine equations
• Heinrich's counterexample to Azevedo's conjecture
• Tjurina number of a generic irreducible curve singularity
• On a conjecture of Azevedo
• Analogs of Gröbner bases in polynomial rings over a ring
• Standard bases in power series rings: Uniqueness and superfluous critical pairs
• Standard bases for local rings of branches and their modules of differentials
• Algorithm for the semigroup of a space curve singularity
• Differentialmoduln eindimensionaler lokaler Ringe
• Sur les modules des singularités des courbes planes
• Classification of Algebroid Plane Curves with Semigroup ⟨6, 9, 19⟩
• Studies in Equisingularity I Equivalent Singularities of Plane Algebroid Curves
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