Frobenius vectors, Hilbert series and gluings

Abdallah Assi (1) , Pedro A. García-Sánchez (2) , Ignacio Ojeda (3)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 Departamento de Algebra
3 Departamento de Matemáticas, Universidad de Extremadura

Let S_1 and S_2 be two affine semigroups and let S be the gluing of S_1 and S_2. Several invariants of S are then related to those of S_1 and S_2; we review some of the most important properties preserved under gluings. The aim of this paper is to prove that this is the case for the Frobenius vector and the Hilbert series. Applications to complete intersection affine semigroups are also given.

Mots clés: Affine semigroup; gluing; Frobenius vector; Hilbert series

Domaines: Algèbre commutative [math.AC]; Combinatoire [math.CO]

Abdallah Assi, Pedro A. García-Sánchez, Ignacio Ojeda. Frobenius vectors, Hilbert series and gluings. 2013. ⟨hal-00881276⟩