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arXiv · 1405.2545

Isogenies of Jacobians

V. Marcucci·J. C. Naranjo·G. P. Pirola
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Abstract

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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V. Marcucci, J. C. Naranjo, G. P. Pirola. 2014-05-11. Isogenies of Jacobians. https://arxiv.org/abs/1405.2545

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