Klein coverings over hyperelliptic genus 3 curves
Abstract
We characterize the moduli space of \'etale Klein coverings (i.e. Galois with deck group Z22) of hyperelliptic curves of genus 3. We prove that the Prym map on each component is injective. As an application, we show that the Prym map of \'etale Klein coverings of genus 3 curves is generically finite.
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