Moduli spaces of vector bundles on a singular rational ruled surface

Usha N. Bhosle; Indranil Biswas

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arXiv · 1509.03384

Moduli spaces of vector bundles on a singular rational ruled surface

Usha N. Bhosle·Indranil Biswas

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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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BibTeX RIS

Usha N. Bhosle, Indranil Biswas. 2015-09-11. Moduli spaces of vector bundles on a singular rational ruled surface. https://arxiv.org/abs/1509.03384

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