arXiv subjects

I. Macías Tarrío

Publications and source records attributed to I. Macías Tarrío.

4 recordsLinked to original sources

arXiv2026

Some moduli spaces of $α$-stable coherent systems on algebraic surfaces

Let $X$ be a smooth, irreducible, projective algebraic surface, and let $α\in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $α$-stable coherent systems of type $(n; c_{1}, c_{2}, k)$ with $k < n$ on $X$, for sufficiently large values of $α$. We prove that, for $α$ sufficiently large, the moduli space admits a description as a Grassmann bundle over a moduli space of $H$-stable torsion free sheaves. As a consequence, we obtain results on irreducibility, dimension. Our approach relies on establishing a correspondence between $α$-stable coherent systems and extensions of $H$-stable torsion free sheaves by trivial bundles.

math.AG↗

arXiv2025

Higher rank prioritary bundles on ruled surfaces and their global sections

Let $X$ be a ruled surface over a nonsingular curve $C$ of genus $g\geq0$. The main goal of this paper is to construct simple prioritary vector bundles of any rank $r$ on $X$ and to give effective bounds for the dimension of their module of global sections.

math.AG↗

arXiv2024

Clifford's Theorem for Coherent Systems on surfaces

Let X be a smooth irreducible projective surface. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on X.

math.AG↗

arXiv2024

Brill-Noether Theory of stable vector bundles on ruled surfaces

Let X be a ruled surface over a nonsingular curve C of genus $g\geq0$. Let $M_H:=M_{X,H}(2;c_1,c_2)$ be the moduli space of H-stable rank 2 vector bundles E on X with fixed Chern classes $c_i:=c_i(E)$ for $i=1,2$. The main goal of this paper is to contribute to a better understanding of the geometry of the moduli space $M_H$ in terms of its Brill-Noether locus $W_H^k(2;c_1,c_2)$, whose points correspond to stable vector bundles in $M_H$ having at least k independent sections. We deal with the non-emptiness of this Brill-Noether locus, getting in most of the cases sharp bounds for the values of k such that $W_H^k(2;c_1,c_2)$ is non-empty.

math.AG↗