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March 23, 2026Advances in Geometry

Decomposition of jacobians of generalized Fermat curves

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Authors

GMGary Martinez-Nuñez

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Overview

The decomposition of the jacobian reveals elliptic curves in generalized Fermat curves, suggesting broader implications for algebraic geometry.

Key Points

  • This research aims to decompose the jacobian variety of generalized Fermat curves and investigate elliptic curves within this context.
  • Derived a decomposition of the jacobian variety for generalized Fermat curves.
  • Extended previous results on Humbert-Edge curves to generalized Fermat curves.
  • Computed the number of elliptic curves resulting from the decomposition for specific cases.
  • Found an explicit decomposition of the jacobian variety.
  • Identified the number of elliptic curves for several generalized Fermat curves.

Cite This Study

Gary Martinez-Nuñez (2026) studied this question.

synapsesocial.com/papers/69c08b9fa48f6b84677f929chttps://doi.org/10.1515/advgeom-2026-0001
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