Moduli spaces of vector bundles on a singular rational ruled surface

2015/09/11 by Usha N. Bhosle, Indranil Biswas, Bhosle, Usha N. +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Primary 14H60 #Secondary 14P99

paper · doi:10.48550/arxiv.1509.03384

openalex publication_date 2015/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study moduli spaces M_X(r,c₁,c₂) parametrizing slope semistable vector bundles of rank r and fixed Chern classes c₁, c₂ on a ruled surface whose base is a rational nodal curve. We show that under certain conditions, these moduli spaces are irreducible, smooth and rational (when non-empty). We also prove that they are non-empty in some cases. We show that for a rational ruled surface defined over real numbers, the moduli space M_X(r,c₁,c₂) is rational as a variety defined over \mathbb R.

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