Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)
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For a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated to such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties. We also consider some special cases of the covering C -> E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of 3 different elliptic curves. Our description is accompanied with explicit numerical examples
CitacióFedorov, Y.; Enolski, V.Z. "Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)". 2014.
Versió de l'editorhttp://arxiv.org/pdf/1411.6143v1