Antonino Ficarra

activity

20212026

most citedUpper bounds for Extremal Betti Numbers of

t

-Spread Strongly Stable Ideals

4 citations · 17 across the 50 of their papers we have counts for

collaborators

54 papers

math.AC2026

Symbolic Rees algebras of complementary edge ideals

Antonino Ficarra, Somayeh Moradi, Yuji Muta

Let $G$ be a finite simple graph on $[n]$ and let $I_{c} (G)$ denote its complementary edge ideal in the polynomial ring $S = K [x_{1}, \dots, x_{n}]$ . We give a combinatorial description, i…

math.AC2026

Serre depth and local cohomology

Antonino Ficarra

We introduce a fundamental homological invariant, called Serre depth, which stratifies Serre's conditions in the same way that depth stratifies the Cohen-Macaulay property. We stud…

math.AC2026

The stable set of associated primes of a complementary edge ideal

Antonino Ficarra

We explicitly determine the associated primes of every power of a complementary edge ideal, prove that they satisfy the persistence property, and compute the $v$ -function. I…

math.AC2025

On the gradient of a monomial ideal

Antonino Ficarra

Let $K$ be a field of characteristic zero, let $I \subset S = K [x_{1}, \dots, x_{n}]$ be a homogeneous ideal, and let $\partial (I)$ be its gradient ideal. We study the relationship betwe…

math.AC2025

Rees algebras of complementary edge ideals

Antonino Ficarra, Somayeh Moradi

In this paper we investigate the Rees algebras of squarefree monomial ideals $I \subset S = K [x_{1}, \dots, x_{n}]$ generated in degree $n - 2$ , where $K$ is a field. Every such ideal arises…

math.AC2025

Polymatroidal ideals and their asymptotic syzygies

Antonino Ficarra, Dancheng Lu

Let $I$ be a polymatroidal ideal. In this paper, we study the asymptotic behavior of the homological shift ideals of powers of polymatroidal ideals. We prove that the first homolog…

math.AC2025

Complementary edge ideals

Antonino Ficarra, Somayeh Moradi

Let $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring over a field $K$ and $I \subset S$ be a squarefree monomial ideal generated in degree $n - 2$ . Motivated by the remarkable behavior of…

math.AC2025

Stanley-Reisner ideals with linear powers

Antonino Ficarra, Somayeh Moradi

Let $S = K [x_{1}, \dots, x_{n}]$ be the standard graded polynomial ring over a field $K$ . In this paper, we address and completely solve two fundamental open questions in Commutative A…

math.AC2025

Principal vector-spread Borel ideals

Marilena Crupi, Antonino Ficarra, Ernesto Lax

We study the class of squarefree principal vector-spread Borel ideals. We compute the minimal primary decomposition of these ideals and thereby we prove that they are sequentially…

math.CO2025

Generalizing blocking semiovals in finite projective planes

Marilena Crupi, Antonino Ficarra

Blocking semiovals and the determination of their (minimum) sizes constitute one of the central research topics in finite projective geometry. In this article we introduce the conc…

math.AC2025

Comparison of stability indices of powers of graded ideals

Antonino Ficarra, Emanuele Sgroi

In this paper, we compare the index of ass-stability $astab (I)$ and the index of $v$ -stability $vstab (I)$ of powers of a graded ideal $I$ . We prove that $\text…

math.AC2025

Edge ideals whose all matching powers are bi-Cohen-Macaulay

Marilena Crupi, Antonino Ficarra

We classify all graphs $G$ satisfying the property that all matching powers $I (G)^{[k]}$ of the edge ideal $I (G)$ are bi-Cohen-Macaulay for $1 \leq k \leq ν (G)$ , where $ν (G)$ is the max…

math.AC2025

Symbolic powers of polymatroidal ideals

Antonino Ficarra, Somayeh Moradi

In this paper, we investigate the componentwise linearity and the Castelnuovo-Mumford regularity of symbolic powers of polymatroidal ideals. For a polymatroidal ideal $I$ , we conje…

math.AC2025

Algebraic study on permutation graphs

Antonino Ficarra, Somayeh Moradi

Let $G$ be a permutation graph. We show that $G$ is Cohen-Macaulay if and only if $G$ is unmixed and vertex decomposable. When this is the case, we obtain a combinatorial descripti…

math.AC2025

Cotangent functors and Herzog's last theorem

Antonino Ficarra

We present the theory of cotangent functors following the approach of Palamodov, and a conjecture of Herzog relating the vanishing of certain cotangent functors to the property of…

math.AC2025

Edge ideals and their asymptotic syzygies

Antonino Ficarra, Ayesha Asloob Qureshi

Let $G$ be a finite simple graph, and let $I (G)$ denote its edge ideal. In this paper, we investigate the asymptotic behavior of the syzygies of powers of edge ideals through the l…

math.AC2024

Sortable simplicial complexes and their associated toric rings

Antonino Ficarra, Somayeh Moradi

Let $Γ$ be a $d$ -flag sortable simplicial complex. We consider the toric ring $R_{Γ} = K [x_{F} t : F \in Γ]$ and the Rees algebra of the facet ideals $I (Γ^{[i]})$ of pure skeletons of…

math.AC2024

The homological shift algebra of a monomial ideal

Antonino Ficarra, Ayesha Asloob Qureshi

Let $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring over a field $K$ , and let $I \subset S$ be a monomial ideal. In this paper, we introduce the $i$ th \textit{homological shift algebras…

math.AC2024★ 1 cited

Componentwise linear symbolic powers of edge ideals and Minh's conjecture

Antonino Ficarra, Somayeh Moradi, Tim Römer

In this paper, we study the componentwise linearity of symbolic powers of edge ideals. We propose the conjecture that all symbolic powers of the edge ideal of a cochordal graph are…

math.AC2024★ 1 cited

Monomial ideals whose all matching powers are Cohen-Macaulay

Antonino Ficarra, Somayeh Moradi

In the present paper, we aim to classify monomial ideals whose all matching powers are Cohen-Macaulay. We especially focus our attention on edge ideals. The Cohen-Macaulayness of t…

math.AC2024

A new proof of the Herzog-Hibi-Zheng theorem

Antonino Ficarra

We give a new, elementary proof of the celebrated Herzog-Hibi-Zheng theorem on powers of quadratic monomial ideals.

math.AC2024

The canonical trace of Cohen-Macaulay algebras of codimension 2

Antonino Ficarra

In the present paper, we investigate a conjecture of Jürgen Herzog. Let $S$ be a local regular ring with residue field $K$ or a positively graded $K$ -algebra, $I \subset S$ be a per…

math.AC2024

The $v$ -function of powers of sums of ideals

Antonino Ficarra, Pedro Macias Marques

Let $K$ be a field, $I \subset R = K [x_{1}, \dots, x_{n}]$ and $J \subset T = K [y_{1}, \dots, y_{m}]$ be graded ideals. Set $S = R \otimes_{K} T$ and let $L = I S + J S$ . The behaviour of the $v$ -functio…

math.AC2024

Bounds on Dao numbers and applications to regular local rings

Antonino Ficarra, Cleto B. Miranda-Neto, Douglas S. Queiroz

The so-called Dao numbers are a sort of measure of the asymptotic behaviour of full properties of certain product ideals in a Noetherian local ring $R$ with infinite residue field…

Symbolic Rees algebras of complementary edge ideals

Serre depth and local cohomology

The stable set of associated primes of a complementary edge ideal

On the gradient of a monomial ideal

Rees algebras of complementary edge ideals

Polymatroidal ideals and their asymptotic syzygies

Complementary edge ideals

Stanley-Reisner ideals with linear powers

Principal vector-spread Borel ideals

Generalizing blocking semiovals in finite projective planes

Comparison of stability indices of powers of graded ideals

Edge ideals whose all matching powers are bi-Cohen-Macaulay

Symbolic powers of polymatroidal ideals

Algebraic study on permutation graphs

Cotangent functors and Herzog's last theorem

Edge ideals and their asymptotic syzygies

Sortable simplicial complexes and their associated toric rings

The homological shift algebra of a monomial ideal

Componentwise linear symbolic powers of edge ideals and Minh's conjecture

Monomial ideals whose all matching powers are Cohen-Macaulay

A new proof of the Herzog-Hibi-Zheng theorem

The canonical trace of Cohen-Macaulay algebras of codimension 2

The v-function of powers of sums of ideals

Bounds on Dao numbers and applications to regular local rings

The $v$ -function of powers of sums of ideals