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We introduce the notion of star gluing of numerical semigroups and show that this preserves
the arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure. Next …

We show that any two homogeneous affine semigroups can be glued by embedding them
suitably in a higher dimensional space. As a consequence, we show that the sum of any two …

The aim of this survey is to explore complete intersection monomial curves from a
contemporary perspective. The main goal is to help readers understand the intricate …

Abstract A semigroup⟨ C⟩ in N n is a gluing of⟨ A⟩ and⟨ B⟩ if its finite set of generators C
splits into two parts, C= k 1 A⊔ k 2 B with k 1, k 2≥ 1, and the defining ideals of the …

A submonoid of N d is of maximal projective dimension (MPD) if the associated affine
semigroup ring has the maximum possible projective dimension. Such submonoids have a …

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …

Given two semigroups ⟨ A ⟩⟨ A⟩ and ⟨ B ⟩⟨ B⟩ in N^ n N n, we wonder when they can
be glued, ie, when there exists a semigroup ⟨ C ⟩⟨ C⟩ in N^ n N n such that the defining …

We study the projective closures of three important families of affine monomial curves in
dimension $4 $, namely the Backelin curve, the Bresinsky curve and the Arslan curve, in …

We collect some open problems about minimal presentations of numerical semigroups and,
more generally, about defining ideals and free resolutions of their semigroup rings and …