Isogenies of Jacobians
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math.AG
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jacobianbabbage-enriques-petriclassicalcodimensionaldegenerationdistinctelementextend
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We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of $\mathcal M_g$ is not isogenous to a distinct Jacobian if $g>3k+4$. We extend this result to $k=1, g\ge 5$ by using degeneration methods.
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