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We study the Prym varieties arising from \'etale cyclic coverings of degree 7over a curve of genus 2. These Prym varieties are products of Jacobians JY x JYof genus 3 curves Y with polarization type D=(1,1,1,1,1,7). We describe thefibers of the Prym map between the moduli space of such coverings and themoduli space of abelian sixfolds with polarization type D, admitting anautomorphism of order 7.

The fibres of the Prym map of \'etale cyclic coverings of degree 7