Real Algebraic and Analytic Geometry Preprint Server

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homepages: http://fraise.univ-brest.fr/~huisman/, http://www.dima.unige.it/~lattarul/

Submission: 2003, March 14.

Abstract:
A real hyperelliptic curve X is said to be Gaussian if there is an automorphism a of the complexification of X such that its complex conjugate automorphism is equal to [-1] a, where [-1] denotes the hyperelliptic involution on the complexification of X. Gaussian curves arise naturally in several contexts, for example when one studies real Jacobians. In the present paper we study the properties of Gaussian curves and we describe their moduli spaces.

Mathematics Subject Classification (2000): 14H15, 14H37, 14P99, 30F50.

Keywords and Phrases: hyperelliptic curve, automorphism, moduli space, ramified double covering.

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