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On the moduli of logarithmic connections on elliptic curves

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Abstract

We describe moduli spaces of logarithmic rank 2 connections on elliptic curves with \(n \ge 1\) poles and generic residues. In particular, we generalize a previous work by the first and second named authors. Our main approach is to analyze the underlying parabolic bundles; their stability and instability play a major role.

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Acknowledgements

We warmly thank the anonymous referee for many useful comments and suggestions.

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Authors and Affiliations

  1. Universidade Federal Fluminense, UFF, Rua Alexandre Moura 8, Niterói, RJ, Brazil

    Thiago Fassarella & Alan Muniz

  2. Univ Rennes, CNRS, IRMAR, UMR 6625, 35000, Rennes, France

    Frank Loray

  3. Universidade Federal do Espírito Santo, UFES, Av. Fernando Ferrari 514, Vitória, ES, Brasil

    Alan Muniz

Authors
  1. Thiago Fassarella
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  2. Frank Loray
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  3. Alan Muniz
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Correspondence to Thiago Fassarella.

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The second author is supported by CNRS, and ANR-16-CE40-0008 project “Foliage”. This work was conducted during the postdoctoral periods of the third author at UFES and UFF, when he was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. The authors also thank Brazilian-French Network in Mathematics and CAPES-COFECUB project MA 932/19.

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Fassarella, T., Loray, F. & Muniz, A. On the moduli of logarithmic connections on elliptic curves. Math. Z. 301, 4079–4118 (2022). https://doi.org/10.1007/s00209-022-03041-4

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