Proportionally modular affine semigroups

Abstract

This work introduces a new kind of semigroup of ${\mathbb{N}}^p$ called proportionally modular affine semigroup. These semigroups are defined by modular Diophantine inequalities and they are a generalization of proportionally modular numerical semigroups. We prove they are finitely generated and we give an algorithm to compute their minimal generating sets. We also specialise on the case $p=2$. For this case, we provide a faster algorithm to compute their minimal system of generators and we prove they are Cohen-Macaulay and Buchsbaum. Besides, the Gorenstein property is charactized, and their (minimal) Fröbenius vectors are determinated.

References in corpus (1)

• Frobenius vectors, Hilbert series and gluings