Low-degree points on Hurwitz-Klein curves

Author:

Tzermias Pavlos

Abstract

We investigate low-degree points on the Fermat curve of degree 13, the Snyder quintic curve and the Klein quartic curve. We compute all quadratic points on these curves and use Coleman’s effective Chabauty method to obtain bounds for the number of cubic points on each of the former two curves.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference21 articles.

1. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences];Arbarello, E.,1985

2. Effective Chabauty;Coleman, Robert F.;Duke Math. J.,1985

3. Torsion points on abelian étale coverings of 𝑃¹-{0,1,∞};Coleman, Robert F.;Trans. Amer. Math. Soc.,1989

4. M. Coppens: A study of the schemes 𝑊ₑ¹ of smooth plane curves, in Proc. 1st Belgian-Spanish Week on Algebra and Geometry, R.U.C.A (1988), 29-63.

5. Points of low degree on smooth plane curves;Debarre, Olivier;J. Reine Angew. Math.,1994

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