A. Katsabekis

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20242026

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math.AC2026

Admissible bases and generic lattice ideals

Anargyros Katsabekis

We introduce the notion of an admissible basis for rank-three positive lattices in $Z^{4}$ , namely a $Z$ -basis ${c_{1}, c_{2}, c_{3}}$ satisfying three…

math.AC2026

On complete intersection projective closures of monomial curves

Anargyros Katsabekis

In this paper, we study the complete intersection property of projective closures of affine monomial curves. For monomial curves in the four-dimensional affine space, we give a com…

math.AC2026

Radical splittings of toric ideals

Anargyros Katsabekis, Apostolos Thoma

Let $I_{A} \subset K [x_{1}, \dots, x_{n}]$ be a toric ideal. In this paper, we provide a necessary and sufficient condition for the toric variety $V (I_{A})$ , over an algebraically closed fi…

math.AC2025

Splittings of toric ideals of graphs

Anargyros Katsabekis, Apostolos Thoma

Let $G$ be a simple graph on the vertex set ${v_{1}, \dots, v_{n}}$ . An algebraic object attached to $G$ is the toric ideal $I_{G}$ . We say that $I_{G}$ is subgraph splittable if ther…

math.AC2024

Toric splittings

Anargyros Katsabekis, Apostolos Thoma

The toric ideal $I_{A}$ is splittable if it has a toric splitting; namely, if there exist toric ideals $I_{A_{1}}, I_{A_{2}}$ such that $I_{A} = I_{A_{1}} + I_{A_{2}}$ and $I_{A_{i}} \neq = I_{A}$ for…

math.AC2024

Cohen-Macaulayness of associated graded rings of Gorenstein monomial curves

Anargyros Katsabekis

Let $C$ be a Gorenstein noncomplete intersection monomial curve in the 4-dimensional affine space with defining ideal $I (C)$ . In this article, we use the minimal generating set of…