Decomposition of jacobians of generalized Fermat curves

Abstract 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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Publication Details

Journal
Advances in Geometry
Published
2026-03-21
DOI
https://doi.org/10.1515/advgeom-2026-0001
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
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article

Decomposition of jacobians of generalized Fermat curves

Gary Martinez-Nuñez
Advances in Geometry
Algebraic Geometry and Number Theory
article

Decomposition of jacobians of generalized Fermat curves

Gary Martinez-Nuñez
article en

Abstract

Abstract 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.

Advances in Geometry
Universidad de Santiago de Chile (CL), University of Chile (CL)
Openalex Percentile: Top 11%
Algebraic Geometry and Number Theory
DOISourceOpenAlex
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