G. Favacchio

activity

20132024

most citedSplittings of Toric Ideals

9 citations · 14 across the 20 of their papers we have counts for

collaborators

23 papers

math.AG2024

Finite sets of points in $P^{4}$ with special projection properties

Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4

In this note we introduce the notion of $(b, d)$ -geprofi sets and study their basic properties. These are sets of $b d$ points in $P^{4}$ whose projection from a general point…

math.AC2024

On the Weak Lefschetz Property for certain ideals generated by powers of linear forms

Giuseppe Favacchio, Juan Migliore

Ideals $I \subseteq R = k [P^{n}]$ generated by powers of linear forms arise, via Macaulay duality, from sets of fat points $X \subseteq P^{n}$ . Properties of $R / I$ are conn…

math.AG2023

Geproci sets on skew lines in $P^{3}$ with two transversals

Luca Chiantini, Pietro De Poi, Lucja Farnik +6

The purpose of this work is to pursue classification of geproci sets. Specifically we classify $[m, n]$ -geproci sets which consist of $m = 4$ points on each of $n$ skew lines, assumin…

math.AG2023

Combinatorics of skew lines in $P^{3}$ with an application to algebraic geometry

Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4

This article introduces a previously unrecognized combinatorial structure underlying configurations of skew lines in $P^{3}$ , and reveals its deep and surprising connection…

math.AG2023

The Waldschmidt constant of a standard $k$ -configuration in $P^{2}$

Maria Virginia Catalisano, Giuseppe Favacchio, Elena Guardo +1

A $k$ -configuration of type $(d_{1}, \dots, d_{s})$ is a specific set of points in $P^{2}$ that has a number of algebraic and geometric properties. For example, the graded Bett…

math.AG2023

On the classification of certain geproci sets

Luca Chiantini, Lucja Farnik, Giuseppe Favacchio +4

In this short note we develop new methods toward the ultimate goal of classifying geproci sets in $P^{3}$ . We apply these methods to show that among sets of $16$ points distr…

math.AG2022★ 1 cited

Configurations of points in projective space and their projections

Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4

We call a set of points $Z \subset P_{C}^{3}$ an $(a, b)$ -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point $P$ …

math.AG2021

Rational normal curves and Hadamard products

Enrico Carlini, Maria Virginia Catalisano, Giuseppe Favacchio +1

Given $r > n$ general hyperplanes in $P^{n},$ a star configuration of points is the set of all the $n$ -wise intersection of them. We introduce {\it contact star configurations}…

math.AC2021

Steiner Configurations ideals: containment and colouring

Edoardo Ballico, Giuseppe Favacchio, Elena Guardo +2

Given a homogeneous ideal $I \subseteq k [x_{0}, \dots, x_{n}]$ , the Containment problem studies the relation between symbolic and regular powers of $I$ , that is, it asks for which pair $…

math.AC2020

The ACM property for unions of lines in $P^{1} \times P^{2}$

Giuseppe Favacchio, Juan Migliore

This paper examines the Arithmetically Cohen-Macaulay (ACM) property for certain codimension 2 varieties in $P^{1} \times P^{2}$ called sets of lines in $\mathbb P^1\tim…

math.AG2020

Steiner systems and configurations of points

Edoardo Ballico, Giuseppe Favacchio, Elena Guardo +1

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System $S (t, n, v)$ we associate two…

math.AC2020

Regularity and h-polynomials of toric ideals of graphs

Giuseppe Favacchio, Graham Keiper, Adam Van Tuyl

For all integers $4 \leq r \leq d$ , we show that there exists a finite simple graph $G = G_{r, d}$ with toric ideal $I_{G} \subset R$ such that $R / I_{G}$ has (Castelnuovo-Mumford) regula…

math.AG2020

Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces

Giuseppe Favacchio, Elena Guardo, Brian Harbourne +1

If $X \subset P^{n}$ is a reduced subscheme, we say that $X$ admits an unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of having multiplicity $m$ …

math.AC2019★ 9 cited

Splittings of Toric Ideals

Giuseppe Favacchio, Johannes Hofscheier, Graham Keiper +1

Let $I \subseteq R = K [x_{1}, \dots, x_{n}]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric…

math.AC2018

In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals

Erin Bela, Giuseppe Favacchio, Nghia Tran

The aim of this paper is to study the associated primes of powers of squarefree monomial ideals. Hypergraphs and squarefree monomial ideals are strongly connected. The cover ideal…

math.AC2017

A numerical property of Hilbert functions and lex segment ideals

Giuseppe Favacchio

We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segm…

math.AG2017

Multiprojective spaces and the arithmetically Cohen-Macaulay property

Giuseppe Favacchio, Juan Migliore

In this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for $P^{1} \times P^{1}$ a…

math.AG2017★ 1 cited

Special arrangements of lines: codimension two ACM varieties in $P^{1} \times P^{1} \times P^{1}$

Giuseppe Favacchio, Elena Guardo, Beatrice Picone

In this paper we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimensional two arithmetically Cohen-Macaulay (ACM) varieties…

math.AG2017★ 1 cited

On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces

Giuseppe Favacchio, Elena Guardo, Juan Migliore

Published version: We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially $(P^{1})^{n}$ . A combinatorial char…

math.AC2016

The Hilbert function of bigraded algebras in $k [P^{1} \times P^{1}]$

Giuseppe Favacchio

We classify the Hilbert functions of bigraded algebras in $k [x_{1}, x_{2}, y_{1}, y_{2}]$ introducing a numerical function called Ferrers function.

math.AG2016★ 1 cited

The minimal free resolution of fat almost complete intersections in $P^{1} \times P^{1}$

Giuseppe Favacchio, Elena Guardo

A current research theme is to compare symbolic powers of an ideal $I$ with the regular powers of $I$ . In this paper, we focus on the case that $I = I_{X}$ is an ideal defining an almo…

math.AC2014

Tower sets and other configurations with the Cohen-Macaulay property

Giuseppe Favacchio, Alfio Ragusa, Giuseppe Zappalà

Some well-known arithmetically Cohen-Macaulay configurations of linear varieties in $P^{r}$ as $k$ -configurations, partial intersections and star configurations are generali…

math.AC2013★ 1 cited

On the weak Lefschetz Property of graded modules over $K [x, y]$

Giuseppe Favacchio, Phong Dinh Thieu

It is known that graded cyclic modules over $S = K [x, y]$ have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over $S$ . The purpose of this note is to stud…

Finite sets of points in P4 with special projection properties

On the Weak Lefschetz Property for certain ideals generated by powers of linear forms

Geproci sets on skew lines in P3 with two transversals

Combinatorics of skew lines in P3 with an application to algebraic geometry

The Waldschmidt constant of a standard k-configuration in P2

On the classification of certain geproci sets

Configurations of points in projective space and their projections

Rational normal curves and Hadamard products

Steiner Configurations ideals: containment and colouring

The ACM property for unions of lines in P1×P2

Steiner systems and configurations of points

Regularity and h-polynomials of toric ideals of graphs

Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces

Splittings of Toric Ideals

In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals

A numerical property of Hilbert functions and lex segment ideals

Multiprojective spaces and the arithmetically Cohen-Macaulay property

Special arrangements of lines: codimension two ACM varieties in P1×P1×P1

On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces

The Hilbert function of bigraded algebras in k[P1×P1]

The minimal free resolution of fat almost complete intersections in P1×P1

Tower sets and other configurations with the Cohen-Macaulay property

On the weak Lefschetz Property of graded modules over K[x,y]

Finite sets of points in $P^{4}$ with special projection properties

Geproci sets on skew lines in $P^{3}$ with two transversals

Combinatorics of skew lines in $P^{3}$ with an application to algebraic geometry

The Waldschmidt constant of a standard $k$ -configuration in $P^{2}$

The ACM property for unions of lines in $P^{1} \times P^{2}$

Special arrangements of lines: codimension two ACM varieties in $P^{1} \times P^{1} \times P^{1}$

The Hilbert function of bigraded algebras in $k [P^{1} \times P^{1}]$

The minimal free resolution of fat almost complete intersections in $P^{1} \times P^{1}$

On the weak Lefschetz Property of graded modules over $K [x, y]$