Fixed points of automorphisms of real algebraic curves

2006/09/28 by Jean-Philippe Monnier, Monnier, Jean-Philippe
Mathematics · #14H37 #14P25 #14P99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H37 #msc:14P25 #msc:14P99

paper · pdf · doi:10.48550/arxiv.math/0609811

arxiv created 2006/09/28 · arxiv updated 2009/12/01

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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