Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2006, September 28.

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.

Mathematics Subject Classification (2000): 14H37, 14P25, 14P99.

Keywords and Phrases: Automorphisms, Real algebraic curves.

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