Prym maps of cyclic coverings of hyperelliptic curves
Abstract
We prove that the Prym map corresponding to \'etale cyclic coverings of hyperelliptic curves is injective whenever the degree of the covering d ≥ 6 is not a power of an odd prime. For other degrees d≥ 9, we show that the Prym map is generically injective. In particular, we complete the study of Prym maps of \'etale cyclic coverings of genus 2 curves.
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