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ABSTRACT
We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of genera for which there is a curve with completely decomposable Jacobian. These examples greatly extend the list given by Ekedahl and Serre of genera containing such curves, and provide more evidence for a positive answer to two questions they asked. Additionally, we produce new examples of families of curves, all of which have completely decomposable Jacobian varieties. These families relate to questions about special subvarieties in the moduli space of principally polarized abelian varieties.
Acknowledgments
The second author is very grateful to Grinnell College, where the final version of this article was written, for its hospitality and the kindness of all its people. Many thanks to the anonymous referees for the time they took to carefully read our article and make a number of suggestions which greatly improved the exposition.
Funding
This study is partially supported by Fondecyt Grant 1140507 and Conicyt PIA ACT1415. The first author was also supported by a Harris Faculty Fellowship through Grinnell College.