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

2025/11/20 by Laura Costa, Costa, L., I. Macías Tarrío +3
Mathematics · #14D20 #14H60 #14J60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.16581

openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth, irreducible, projective algebraic surface, and let α∈ 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; c₁, c₂, 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.

Citations

• Clifford's Theorem for Coherent Systems on surfaces
• Stability and cohomology of kernel bundles on projective space
• Higher rank Brill-Noether theory and coherent systems: Open questions
• Coherent systems on the projective line
• Moduli spaces of coherent systems of small slope on algebraic curves
• On the geometry of moduli spaces of coherent systems on algebraic curves
• Coherent systems of genus 0
• Coherent systems and Brill-Noether theory
• Moduli of Brill-Noether pairs on algebraic curves
• Stable pairs, linear systems and the Verlinde formula

Related

• On the geometry of moduli spaces of coherent systems on algebraic curves
• Moduli spaces of coherent systems of small slope on algebraic curves
• On the Moduli Space of Coherent Systems of Type (2, c₁, c₂, 2) on Projective Plane
• Coherent systems of genus 0
• Existence of coherent systems