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Fixed points of automorphisms of real algebraic curves

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Abstract

We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism and the maximum order of an abelian group of automorphisms of a real curve. We also bound the full group of automorphisms of a real hyperelliptic curve.

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Authors and Affiliations

  1. Département de Mathématiques, Université d’Angers, 2, Bd. Lavoisier, 49045, Angers cedex 01, France

    Jean-Philippe Monnier

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  1. Jean-Philippe Monnier
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Correspondence to Jean-Philippe Monnier.

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Work supported by the European Community’s Human Potential Programme under contract HPRN-CT-2001-00271, RAAG.

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Monnier, JP. Fixed points of automorphisms of real algebraic curves. manuscripta math. 124, 459–480 (2007). https://doi.org/10.1007/s00229-007-0117-z

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  • DOI: https://doi.org/10.1007/s00229-007-0117-z

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