Imaginary automorphisms on real hyperelliptic curves. (English) Zbl 1077.14038
A real hyperelliptic curve \(X\) is said to be Gaussian if there is an automorphism \(\alpha : X_{\mathbb C} \to X_{\mathbb C}\) such that \(\bar{\alpha } = [-1]_{\mathbb C}\circ \alpha\), where \([-1]\) denotes the hyperelliptic involution. Gaussian hyperelliptic curves occur in several contexts (e.g. in the study of real Jacobian). Here the authors prove that a real hyperelliptic curve is Gaussian if and only if it is uniquely determined by its branch locus. They describe their moduli spaces.For many properties of real hyperelliptic curves, see M. Lattarulo [Commun. Algebra 31, 1679–1703 (2003; Zbl 1059.14070)].
Reviewer: Edoardo Ballico (Povo)
MSC:
| 14H15 | Families, moduli of curves (analytic) |
| 14H37 | Automorphisms of curves |
| 14P99 | Real algebraic and real-analytic geometry |
| 30F50 | Klein surfaces |
Citations:
Zbl 1059.14070References:
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