Rosa M. Miró-Roig

activity

20212026

collaborators

20 papers

cond-mat.dis-nn2026

Resolving Structural Uncertainty in Stochastic Dynamical Systems via Ensemble-Based Bayesian Inference

Francesco Zambelli, Valeria D'Andrea, Manlio De Domenico

Recovering the interaction structure of complex stochastic dynamical systems from sparse time-series observations is an inherently ill-posed inverse problem. The posterior over net…

math.AC2026

Artinian Gorenstein algebras with Macaulay dual generator with fixed Waring rank

Janaine Martins, Rosa M. Miró-Roig

In this paper, we prove that the Artinian Gorenstein $K$ -algebra $A_{F_{s}}$ of codimension $n$ , socle degree $d$ and Macaulay dual generator $F_s := \ell_1^d + \dots + \ell…

math.AG2025

Smoothings of lci proper schemes

Barbara Fantechi, Rosa M. Miró-Roig

We give criteria for the existence of geometric smoothings of a proper lci scheme or a DM stack $X$ as well as for a polarized lci scheme $(X, L)$ , without assuming that $X$ is redu…

math.AC2025

Jordan type of full Perazzo algebras

Pedro Macias Marques, Rosa M. Miró-Roig, Josep Pérez

In this paper, we compute all possible Jordan types of linear forms $ℓ$ in any full Perazzo algebra $A$ . In some cases we are also able to compute the corresponding Jordan degre…

math.AG2025

Weak Lefschetz property of equigenerated complete intersections. Applications

Valentina Beorchia, Rosa Maria Miró-Roig

In this paper, we prove that any Artinian complete intersection homogeneous ideal $I$ in $K [x_{0}, \dots, x_{n}]$ generated by $n + 1$ forms of degree $d \geq 2$ satisfies the weak Lefschet…

math.AC2025

Complete intersection algebras with binomial Macaulay dual generator

Roberta Di Gennaro, Rosa Maria Miró-Roig

In this paper, we characterize all Artinian complete intersection $K$ -algebras $A_{F}$ whose Macaulay dual generator $F$ is a binomial. In addition, we prove that such complete inter…

math.AC2025

Artinian Gorenstein algebras with binomial Macaulay dual generator

Nasrin Altafi, Rodica Dinu, Sara Faridi +4

This paper initiates a systematic study for key properties of Artinian Gorenstein $K$-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all…

math.AC2025

New families of Artinian Gorenstein algebras with the weak Lefschetz property

Nasrin Altafi, Rodica Dinu, Shreedevi K. Masuti +3

We construct new families of Artinian Gorenstein graded $K$ -algebras of arbitrary codimension having binomial Macaulay dual generators and satisfying the weak or the strong Lefsche…

math.AG2025

Saito's theorem revisited and application to free pencils of hypersurfaces

Roberta Di Gennaro, Rosa Maria Miró-Roig

A hypersurface $X \subset P^{n}$ is said to be free if its associated sheaf $T_{X}$ of vector fields tangent to $X$ is a free $O_{P^{n}}$ -module. So far few exa…

math.AG2025

Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies

Aline V. Andrade, Valentina Beorchia, Alexandru Dimca +1

We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V \subset P^{n}$ with only isolated singularities and the nature of its si…

math.AC2025

Betti numbers of full Perazzo algebras

Rosa Maria Miró-Roig, Josep Pérez

In this paper we prove that any full Perazzo algebra $A_{F}$ , whose Macaulay dual generator is a Perazzo form $F \in K [X_{0}, \dots, X_{n}, U_{1}, \dots, U_{m}]_{d}$ with $n + 1 = (m - 1 d + m - 2)$ ,…

math.AG2025

Characterization of linear spaces of matrices of constant rank from syzygy bundles

Simone Marchesi, Rosa Maria Miró-Roig

In this work, we characterize matrices of linear forms and constant rank, demonstrating that, under some natural assumptions, they are always associated with a syzygy bundle that f…

math.AG2024

A characterization of quasi-homogeneous singularities of free and nearly free plane curves

Aline V. Andrade, Valentina Beorchia, Rosa M. Miró-Roig

The goal of this paper is to establish a new characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in $P_{C}^{2}$ . Th…

math.AC2024

The weak Lefschetz property for artinian Gorenstein algebras of small Sperner number

Mats Boij, Juan C. Migliore, Rosa Maria Miró-Roig +1

For artinian Gorenstein algebras in codimension four and higher, it is well known that the Weak Lefschetz Property (WLP) does not need to hold. For Gorenstein algebras in codimensi…

math.AC2024

Perazzo $n$ -folds and the weak Lefschetz property

Emilia Mezzetti, Rosa M. Miró-Roig

In this paper, we determine the maximum $h_{ma x}$ and the minimum $h_{min}$ of the Hilbert vectors of Perazzo algebras $A_{F}$ , where $F$ is a Perazzo polynomial of degree $d$ in $n+…

math.AG2024

On the moduli space of simple sheaves on singular K3 surfaces

Barbara Fantechi, Rosa M. Miró-Roig

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new loca…

math.AG2024

Perazzo hypersurfaces and the weak Lefschetz property

Rosa Maria Miró-Roig, Josep Pérez Díez

We deal with Perazzo hypersurfaces $X = V (f)$ in $\PP^{n+2}$ defined by a homogeneous polynomial $f (x_{0}, x_{1}, \dots, x_{n}, u, v) = p_{0} (u, v) x_{0} + p_{1} (u, v) x_{1} + \dots + p_{n} (u, v) x_{n} + g (u, v)$ , where…

math.AG2023

List of Problems

Martina Juhnke-Kubitzke, Rosa M. Miró-Roig

The study of the Lefschetz properties of Artinian graded algebras was motivated by the hard Lefschetz theorem for a smooth complex projective variety, a breakthrough in algebraic t…

math.AG2023

Schur powers of the cokernel of a graded morphism

Jan O. Kleppe, Rosa M. Miró-Roig

Let $φ : F ⟶ G$ be a graded morphism between free $R$ -modules of rank $t$ and $t + c - 1$ , respectively, and let $I_{j} (φ)$ be the ideal generated by the $j \times j$ minors…

math.AG2021

Companion varieties for root systems and Fermat arrangements

Roberta Di Gennaro, Giovanna Ilardi, Rosa Maria Miró-Roig +2

Unexpected hypersurfaces are a brand name for some special linear systems. They were introduced around 2017 and are a field of intensive study since then. They attracted a lot of a…

Resolving Structural Uncertainty in Stochastic Dynamical Systems via Ensemble-Based Bayesian Inference

Artinian Gorenstein algebras with Macaulay dual generator with fixed Waring rank

Smoothings of lci proper schemes

Jordan type of full Perazzo algebras

Weak Lefschetz property of equigenerated complete intersections. Applications

Complete intersection algebras with binomial Macaulay dual generator

Artinian Gorenstein algebras with binomial Macaulay dual generator

New families of Artinian Gorenstein algebras with the weak Lefschetz property

Saito's theorem revisited and application to free pencils of hypersurfaces

Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies

Betti numbers of full Perazzo algebras

Characterization of linear spaces of matrices of constant rank from syzygy bundles

A characterization of quasi-homogeneous singularities of free and nearly free plane curves

The weak Lefschetz property for artinian Gorenstein algebras of small Sperner number

Perazzo n-folds and the weak Lefschetz property

On the moduli space of simple sheaves on singular K3 surfaces

Perazzo hypersurfaces and the weak Lefschetz property

List of Problems

Schur powers of the cokernel of a graded morphism

Companion varieties for root systems and Fermat arrangements

Perazzo $n$ -folds and the weak Lefschetz property