The moduli space of anisotropic Gaussian curves

Abstract

Let X be a real hyperelliptic curve. Its opposite curve X is the curve obtained from X by twisting the real structure on X by the hyperelliptic involution. The curve X is said to be Gaussian if X is isomorphic to X. In an earlier paper, we have studied Gaussian curves having real points [4]. In the present paper we study Gaussian curves without real points, i.e. anisotropic Gaussian curves. We prove that the moduli space of such curves is a reducible connected real analytic subset of the moduli space of all anisotropic hyperelliptic curves, and determine its irreducible components. MSC 2000: 14H15, 14P99, 30F50, 52C35