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Cyclic and Abelian coverings of real varieties

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Abstract

We describe the birational and the biregular theory of cyclic and Abelian coverings between real varieties.

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Notes

  1. It appears esoteric only because we wish to find explicit algebraic formulae for the field extension, instead of using the real version, Theorem 0.1, of Riemann’s existence theorem of [16].

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Acknowledgements

Thanks to a referee for suggestions on how to improve the presentation of the paper.

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Authors and Affiliations

  1. Lehrstuhl Mathematik VIII, Mathematisches Institut der Universität Bayreuth, NW II Universitätsstr. 30, 95447, Bayreuth, Germany

    Fabrizio Catanese & Michael Lönne

  2. Korea Institute for Advanced Study, Hoegiro 87, Seoul, South Korea

    Fabrizio Catanese

  3. Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via Valerio 12/1, 34127, Trieste, Italy

    Fabio Perroni

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  1. Fabrizio Catanese
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  2. Michael Lönne
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  3. Fabio Perroni
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Correspondence to Fabrizio Catanese.

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Dedicated to Slava (Viatcheslav) Kharlamov on the occasion of his 71-st birthday.

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The present work took place in the framework of the ERC Advanced grant n. 340258, ‘TADMICAMT’. Very preliminary results were announced at the Conference ‘Real Algebraic Geometry’, Università de Rennes 1, June 2011. The third author is supported by the national project PRIN 2017SSNZAW 005-PE1 ‘Moduli Theory and Birational Classification’, by the research group GNSAGA of INDAM and by FRA of the University of Trieste.

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Catanese, F., Lönne, M. & Perroni, F. Cyclic and Abelian coverings of real varieties. Math. Ann. 386, 1799–1827 (2023). https://doi.org/10.1007/s00208-022-02439-z

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