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Moduli spaces of vector bundles on a singular rational ruled surface. (English) Zbl 1375.14111

Summary: We study moduli spaces \(M_X(r,c_1,c_2)\) parametrizing slope semistable vector bundles of rank \(r\) and fixed Chern classes \(c_1,c_2\) 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 \(M_X(r,c_1,c_2)\) is rational as a variety defined over \(\mathbb R\).

MSC:

14H60 Vector bundles on curves and their moduli
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14J17 Singularities of surfaces or higher-dimensional varieties
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