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A note on the moduli spaces of holomorphic and logarithmic connections over a compact Riemann surface

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Abstract

Let X be a compact Riemann surface of genus \(g \ge 3\). We consider the moduli space of holomorphic connections over X and the moduli space of logarithmic connections singular over a finite subset of X with fixed residues. We determine the Chow group of these moduli spaces. We compute the global sections of the sheaves of differential operators on ample line bundles and their symmetric powers over these moduli spaces and show that they are constant under certain conditions. We show the Torelli-type theorem for the moduli space of logarithmic connections. We also describe the rational connectedness of these moduli spaces.

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Acknowledgements

The author would like to thank the anonymous referees for helpful comments, numerous suggestions, and corrections.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Anoop Singh

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Correspondence to Anoop Singh.

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Singh, A. A note on the moduli spaces of holomorphic and logarithmic connections over a compact Riemann surface. Ann Glob Anal Geom 62, 579–601 (2022). https://doi.org/10.1007/s10455-022-09864-y

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