Rosa M. Miró-Roig

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20212026

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11 papers · 1 filter

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.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.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.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.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…