arXiv subjects

Nicola Maugeri

Publications and source records attributed to Nicola Maugeri.

5 recordsLinked to original sources

arXiv2022

Properties and applications of the Apéry set of good semigroups in $\mathbb{N}^d$

In this article we discuss some applications of the construction of the Apéry set of a good semigroup in $\mathbb{N}^d$ given in the previous paper [Partition of the complement of good semigroup ideals and Apéry sets, Communications in Algebra, 49, No. 10, 4136-4158 (2021))]. In particular we study: the duality of a symmetric and almost symmetric good semigroup, the Apéry set of non-local good semigroups and the Apéry set of value semigroups of plane curves.

math.CO↗

arXiv2021

Partition of complement of good ideals and Apéry sets

Good semigroups form a class of submonoids of $\mathbb{N}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the description of the Apéry sets of good semigroups. This generalizes to any $d \geq 2$ the results of a recent paper of D'Anna, Guerrieri and Micale, which are proved in the case $d=2$ and only for the standard Apéry set with respect to the smallest nonzero element. Several new results describing good semigroups in $\mathbb{N}^d$ are also provided.

math.CO↗

arXiv2020

The tree of good semigroups in $\mathbb{N}^2$ and a generalization of the Wilf conjecture

In this work, we study good semigroups of $\mathbb{N}^n$ introducing the definition of length and genus for these objects. We show how to count the local good semigroup with a fixed genus. Furthermore, we study the relationships of these concepts with other ones previously defined in the case of good semigroups with two branches.

math.AC↗

arXiv2019

Embedding dimension of a good semigroup

In this paper, we study good semigroups of \mathbb{N}^n, a class of semigroups that contains the value semigroups of algebroid curves with n branches. We give the definition of embedding dimension of a good semigroup showing that, in the case of good semigroups of \mathbb{N}^2, some of its properties agree with the analogue concepts defined for numerical semigroups.

math.AC↗

arXiv2018

An algorithm for computing the Arf closure of an algebroid curve with more than one branch

In this paper, we give a fast algorithm for the computation of the Arf closure of an algebroid curve with more than one branch, generalizing an algorithm presented by Arslan and Sahin for the algebroid branch case.

math.AC↗