Nearly Gorenstein vs almost Gorenstein affine monomial curves

Moscariello, Alessio; Strazzanti, Francesco

doi:10.48550/arxiv.2003.05391

Cited by 2 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. We will use the following characterization proved in [18]: S is nearly Gorenstein if and only if for every minimal generator y of S there exists g ∈ PF(S) such that g + y − g ′ ∈ S for every g ′ ∈ PF(S) \ {g}.…”

Section: Proof Assume By Contradiction That X /mentioning

confidence: 99%

Almost canonical ideals and GAS numerical semigroups

D'Anna¹,

Strazzanti²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We propose the notion of GAS numerical semigroup which generalizes both almost symmetric and 2-AGL numerical semigroups. Moreover, we introduce the concept of almost canonical ideal which generalizes the notion of canonical ideal in the same way almost symmetric numerical semigroups generalize symmetric ones. We prove that a numerical semigroup with maximal ideal M and multiplicity e is GAS if and only if M − e is an almost canonical ideal of M − M . This generalizes a result of Barucci about almost symmetric semigroups and a theorem of Chau, Goto, Kumashiro, and Matsuoka about 2-AGL semigroups. We also study the transfer of the GAS property from a numerical semigroup to its gluing, numerical duplication and dilatation.

show abstract

Section: Proof Assume By Contradiction That X /mentioning

confidence: 99%

Almost canonical ideals and GAS numerical semigroups

D'Anna¹,

Strazzanti²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, nearly Gorenstein rings, which are the object of interest of this paper, have been introduced even more recently by Herzog, Hibi, and Stamate [HHS19] in 2019. Nevertheless, they have already been studied in several contexts, such as zero-dimensional schemes [KLL19], affine semigroup rings [HJS19], and affine monomial curves [MS20]. See also [EGI19,DKT20,Kob20,Rah20] for other related results.…”

Section: Introductionmentioning

confidence: 99%

Nearly Gorenstein cyclic quotient singularities

Caminata

Strazzanti

2020

Beitr Algebra Geom

Self Cite

View full text Add to dashboard Cite

We investigate the nearly Gorenstein property among d-dimensional cyclic quotient singularities $$\Bbbk \llbracket x_1,\dots ,x_d\rrbracket ^G$$ k 〚 x 1 , ⋯ , x d 〛 G , where $$\Bbbk $$ k is an algebraically closed field and $$G\subseteq {\text {GL}}(d,\Bbbk )$$ G ⊆ GL ( d , k ) is a finite small cyclic group whose order is invertible in $$\Bbbk $$ k . We prove a necessary and sufficient condition to be nearly Gorenstein that also allows us to find several new classes of such rings.

show abstract

Nearly Gorenstein vs almost Gorenstein affine monomial curves

Cited by 2 publications

References 22 publications

Almost canonical ideals and GAS numerical semigroups

Almost canonical ideals and GAS numerical semigroups

Nearly Gorenstein cyclic quotient singularities

Contact Info

Product

Resources

About