10 citations · 12 across the 9 of their papers we have counts for
10 papers
Curve singularities with one Puiseux pair and value sets of modules over their local rings
Maria Alberich-Carramiñana, Patricio Almirón, Julio José Moyano-Fernández
In this paper we characterize the value set of the -modules of the form for the local ring associated to a germ of an irreducible plane curve singularity with…
Eliahou number, Wilf function and concentration of a numerical semigroup
Patricio Almirón, Julio José Moyano-Fernández
We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semi…
Limit spectral distribution for non-degenerate hypersurface singularities
Patricio Almirón, Mathias Schulze
We establish Kyoji Saito's continuous limit distribution for the spectrum of Newton non-degenerate hypersurface singularities. Investigating Saito's notion of dominant value in the…
An extension of the Wilf conjecture to semimodules over a numerical semigroup
Patricio Almirón, Julio José Moyano-Fernández
The aim of this paper is to propose an extension of the Wilf conjecture to semimodules over a numerical semigroup through a new approach toward the solution of the Wilf conjecture…
Supersymmetric gaps of a numerical semigroup with two generators
Patricio Almirón, Julio José Moyano-Fernández
In this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries o…
A formula for the conductor of a semimodule of a numerical semigroup with two generators
Patricio Almirón, Julio José Moyano-Fernández
We provide an expression for the conductor of a semimodule of a numerical semigroup with two generators in terms of the syzygy module of and the generators of th…
The 4/3 problem for germs of isolated plane curve singularities
Patricio Almirón
In this survey we overview the different approaches and solutions of a question posed by Dimca and Greuel about the quotient of the Milnor and Tjurina numbers.
On the quotient of Milnor and Tjurina numbers for two-dimensional isolated hypersurface singularities
Patricio Almirón
In this paper we give a complete answer to a question posed by Dimca and Greuel about the quotient of the Milnor and Tjurina numbers of a plane curve singularity. We put this quest…
The minimal Tjurina number of irreducible germs of plane curve singularities
Maria Alberich-Carramiñana, Patricio Almirón, Guillem Blanco +1
In this paper we give a positive answer to a question of Dimca and Greuel about the quotient between the Milnor and the Tjurina numbers for any irreducible germ of plane curve sing…
A note on a question of Dimca and Greuel
Patricio Almirón, Guillem Blanco
In this note we give a positive answer to a question of Dimca and Greuel about the quotient between the Milnor and Tjurina numbers of an isolated plane curve singularity in the cas…