Abstract
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 \(\mathbb {R}\).
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This work was finalized during the first author’s tenure as Raja Ramanna Fellow at the Indian Institute of Science, Bangalore. The second author is supported by J. C. Bose Fellowship.
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Bhosle, U.N., Biswas, I. Moduli spaces of vector bundles on a singular rational ruled surface. Geom Dedicata 180, 399–413 (2016). https://doi.org/10.1007/s10711-015-0108-2
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DOI: https://doi.org/10.1007/s10711-015-0108-2