Gluing and splitting of homogeneous toric ideals
P Gimenez, H Srinivasan - Journal of Algebra, 2025 - Elsevier
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 …
suitably in a higher dimensional space. As a consequence, we show that the sum of any two …
On the Rich Landscape of Complete Intersection Monomial Curves
P Almirón - arXiv preprint arXiv:2411.19260, 2024 - arxiv.org
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 …
contemporary perspective. The main goal is to help readers understand the intricate …
On gluing semigroups in and the consequences
P Gimenez, H Srinivasan - Research in the Mathematical Sciences, 2022 - Springer
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 …
splits into two parts, C= k 1 A⊔ k 2 B with k 1, k 2≥ 1, and the defining ideals of the …
Affine semigroups of maximal projective dimension
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 …
semigroup ring has the maximum possible projective dimension. Such submonoids have a …
On the associated graded ring of semigroup algebras
J Saha, I Sengupta, P Srivastava - Communications in Algebra, 2023 - Taylor & Francis
In this paper, we give a necessary and sufficient condition for the Cohen-Macaulayness of
the associated graded ring of a simplicial affine semigroup using Gröbner basis. We …
the associated graded ring of a simplicial affine semigroup using Gröbner basis. We …
On p-Frobenius of Affine Semigroups
ER García Barroso, JI García-García… - … Journal of Mathematics, 2024 - Springer
This paper studies the p-Frobenius vector of affine semigroups S⊂ N q. Defined with respect
to a graded monomial order, the p-Frobenius vector represents the maximum element with …
to a graded monomial order, the p-Frobenius vector represents the maximum element with …
On the Gluing of germs of complex analytic spaces, Betti numbers and their structure
TH Freitas, JA Lima - arXiv preprint arXiv:2402.12904, 2024 - arxiv.org
In this paper we introduce new classes of gluing of complex analytic spaces germs, called
weakly large, large and strongly large. We give a description of their Poincar\'e series and …
weakly large, large and strongly large. We give a description of their Poincar\'e series and …
Affine Semigroup Algebras And Their Fibered Sums
CY Chan, I Huang, JC Liu - arXiv preprint arXiv:2403.06219, 2024 - arxiv.org
We study affine semigroup rings as algebras over subsemigroup rings. From this relative
viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup …
viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup …
Wilf Inequality is preserved under Gluing of Semigroups
S Singh, H Srinivasan - arXiv preprint arXiv:2306.09876, 2023 - arxiv.org
Wilf Conjecture on numerical semigroups is an inequality connecting the Frobenius number,
embedding dimension and the genus of the semigroup. The conjecture is still open in …
embedding dimension and the genus of the semigroup. The conjecture is still open in …
On gluing semigroups in and the consequences
P Gimenez, H Srinivasan - arXiv preprint arXiv:2202.01189, 2022 - arxiv.org
A semigroup $\langle C\rangle $ in $\mathbb {N}^ n $ is a gluing of $\langle A\rangle $ and
$\langle B\rangle $ if its finite set of generators $ C $ splits into two parts, $ C= k_1A\sqcup …
$\langle B\rangle $ if its finite set of generators $ C $ splits into two parts, $ C= k_1A\sqcup …