We prove that the Prym map corresponding to \'etale cyclic coverings of hyperelliptic curves is injective whenever the degree of the covering $d \geq 6$ is not a power of an odd prime. For other degrees $d\geq 9$, 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.
Categories: math.AG