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A remark on the decomposition of the Jacobian variety of Fermat curves of prime degree

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Abstract

Recently, Barraza–Rojas have described the action of the full automorphisms group on the Fermat curve of degree p, for p a prime integer, and obtained the group algebra decomposition of the corresponding Jacobian variety. In this short note, we observe that the factors in such a decomposition are given by the Jacobian varieties of certain p-gonal curves.

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References

  1. Aoki N.: Simple factors of the Jacobian of a Fermat curve and the Picard number of a product of Fermat curves. Am. J. Math. 113, 779–833 (1991)

    Article  MATH  Google Scholar 

  2. P. Barraza and Anita M. Rojas, The group algebra decomposition of Fermat curves of prime degree, Arch. Math. 104 (2015), 145–155.

  3. Carocca A., Rodríguez Rubí E.: Jacobians with group actions and rational idempotents. J. Algebra 306, 322–343 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. G. González-Diez, On prime Galois coverings of the Riemann sphere, Ann. Mat. Pura Appl. (4) 168 (1995), 1–15.

  5. Kani E., Rosen M.: Idempotent relations and factors of Jacobians. Math. Ann. 284, 307–327 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lange H., Recillas S.: Abelian varieties with group action. J. Reine Angew. Math. 575, 135–155 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Lefschetz S.: On Certain Numerical Invariants of Algebraic Varieties with Application to Abelian Varieties. Transactions of the American Mathematical Society 22, 407–482 (1921)

    Article  MathSciNet  Google Scholar 

  8. Poincaré H.: Sur les fonctions abéliennes, Amer. J. Math. 8, 289–342 (1886)

    Article  MathSciNet  MATH  Google Scholar 

  9. Riera G., Rodríguez Rubí E.: Riemann surfaces and abelian varieties with an automorphism of prime order, Duke Math. J. 69, 199–217 (1993)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática y Estadística, Universidad de La Frontera, Casilla 54-D, 4780000, Temuco, Chile

    Ruben A. Hidalgo & Rubí E. Rodríguez

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  1. Ruben A. Hidalgo
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  2. Rubí E. Rodríguez
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Correspondence to Ruben A. Hidalgo.

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Partially supported by Fondecyt Grants 1150003 and 1141099.

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Hidalgo, R.A., Rodríguez, R.E. A remark on the decomposition of the Jacobian variety of Fermat curves of prime degree. Arch. Math. 105, 333–341 (2015). https://doi.org/10.1007/s00013-015-0815-9

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  • DOI: https://doi.org/10.1007/s00013-015-0815-9

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