Skip to main content
SpringerLink
Log in

A new characterisation of the Fermat curve

  • Published:
Annali di Matematica Pura ed Applicata (1923 -) Aims and scope Submit manuscript

Abstract

This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Duyaguit, C., Miura, K.: On the number of Galois points for plane curves of prime degree. Nihonkai Math. J. 14, 55–59 (2003)

    MathSciNet  Google Scholar 

  2. Fukasawa, S.: Galois points for a plane curve in arbitrary characteristic. In: Proceedings of the IV Iberoamerican Conference on Complex Geometry. Geometriae Dedicata, vol 139, pp. 211–218 (2009)

  3. Fukasawa, S.: Classification of plane curves with infinitely many Galois points. J. Math. Soc. Jpn. 63, 195–209 (2011)

    Article  MathSciNet  Google Scholar 

  4. Fukasawa, S.: On the number of Galois points for a plane curve in characteristic zero. preprint arXiv:1604.01907

  5. Fukasawa, S.: Algebraic curves admitting non-collinear Galois points. Rend. Sem. Mat. Univ. Padova 149, 183–190 (2023)

    Article  MathSciNet  Google Scholar 

  6. Fukasawa, S.: Galois points and rational functions with small value sets. Hiroshima Math. J. (to appear)

  7. Hirschfeld, J.W.P., Korchmáros, G., Torres, F.: Algebraic Curves over a Finite Field. Princeton Univ. Press, Princeton (2008)

    Book  Google Scholar 

  8. Miura, K., Yoshihara, H.: Field theory for function fields of plane quartic curves. J. Algebra 226, 283–294 (2000)

    Article  MathSciNet  Google Scholar 

  9. Silverman, J.H.: The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106. Springer, New York (1986)

    Book  Google Scholar 

  10. Stichtenoth, H.: Algebraic Function Fields and Codes. Universitext, Springer, Berlin (1993)

    Google Scholar 

  11. Yoshihara, H.: Function field theory of plane curves by dual curves. J. Algebra 239, 340–355 (2001)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author is grateful to Professor Takeshi Harui for helpful comments enabling the author to prove Theorem in the case \(d=6\).

Author information

Authors and Affiliations

  1. Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata, 990-8560, Japan

    Satoru Fukasawa

Authors
  1. Satoru Fukasawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Satoru Fukasawa.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The author was partially supported by JSPS KAKENHI Grant Numbers JP19K03438 and JP22K03223.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fukasawa, S. A new characterisation of the Fermat curve. Annali di Matematica 203, 635–646 (2024). https://doi.org/10.1007/s10231-023-01376-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10231-023-01376-1

Keywords

Mathematics Subject Classification

Search

Navigation