The Apéry Set of a Good Semigroup

2018/12/05 by D'Anna, Marco, Guerrieri, Lorenzo, Micale, Vincenzo
#13A18 #13H99 #14H99 #20M25 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.02064

Abstract

We study the Apéry set of good subsemigoups of \mathbb N², a class of semigroups containing the value semigroups of curve singularities with two branches. Even if this set in infinite, we show that, for the Apéry set of such semigroups, we can define a partition in "levels" that allows to generalize many properties of the Apéry set of numerical semigroups, i.e. value semigroups of one-branch singularities.

Related

• Partition of complement of good ideals and Apéry sets
• Properties and applications of the Apéry set of good semigroups in ℕ^d
• The value semigroup of a plane curve singularity with several branches
• Good subsemigroups of \mathbb Nⁿ
• Embedding dimension of a good semigroup