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Prym varieties and fourfold covers

Sevin Recillas·Rubi Rodriguez
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Abstract

We describe the isotypical decomposition of the Jacobian variety JW of the Galois extension W-->T of any fourfold cover of smooth connected irreducible projective complex curves X-->T, in terms of Prym's of intermediate covers. We also compute the degree of the isogenies involved and as a result we obtain new proofs of the bigonal and trigonal constructions. Furthermore, we give examples of families of Jacobians isogenous to a product of Jacobians and of families of Prym varieties isogenous to the product of elliptic curves.

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Sevin Recillas, Rubi Rodriguez. 2003-03-12. Prym varieties and fourfold covers. https://arxiv.org/abs/math/0303155

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