Moduli spaces of vector bundles on a singular rational ruled surface

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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Correspondence to Indranil Biswas.

Additional information

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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Keywords

  • Vector bundles
  • Moduli
  • Singular ruled surface
  • Rationality

Mathematics Subject Classification (2000)

  • Primary 14H60
  • Secondary 14P99