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The decomposition of the jacobian reveals elliptic curves in generalized Fermat curves, suggesting broader implications for algebraic geometry.
We give a decomposition of the jacobian variety of a generalized Fermat curve. This extends a result obtained by Auffarth, Lucchini Arteche and Rojas on Humbert–Edge curves, which are a particular case of generalized Fermat curves. We also compute the number of elliptic curves appearing in the decomposition for some of these curves.
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Gary Martinez-Nuñez (2026) studied this question.
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