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The curve Yn = Xℓ(Xm + 1) over finite fields II

  • Saeed Tafazolian EMAIL logo and Fernando Torres
Published/Copyright: June 24, 2021
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Advances in Geometry
From the journal Advances in Geometry Volume 21 Issue 3

Abstract

Let F be the finite field of order q2. In this paper we continue the study in [24], [23], [22] of F-maximal curves defined by equations of type yn=xℓ(xm+1). New results are obtained via certain subcovers of the nonsingular model of vN=ut2−u where q = tα, α ≥ 3 is odd and N = (tα + 1)/(t + 1). We observe that the case α = 3 is closely related to the Giulietti–Korchmáros curve.

Keywords: Finite field; maximal curve; Kummer extension
MSC 2010: 11G20; 11M38; 14G15; 14H25

Funding statement: The authors were in part supported respectively by FAPESP/SP-Brazil (Grant 2017/19190-5) and by CNPq-Brazil (Grant 310623/2017-0)

Acknowledgements

The authors hearty thank the referee for her/ his valuable suggestions that helped them to improve the manuscript. In addition, F. Torres would like to thank P. Chacón for her constant support and friendship.

  1. Communicated by: G. Korchmáros

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Received: 2019-09-24
Revised: 2020-01-06
Published Online: 2021-06-24
Published in Print: 2021-07-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On vector bundles over reducible curves with a node
  3. Inscribed rectangle coincidences
  4. 𝔽p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
  5. Tetrahedral cages for unit discs
  6. When is M0,n(ℙ1,1) a Mori dream space?
  7. Rank-one isometries of CAT(0) cube complexes and their centralisers
  8. Wall-crossing in genus-zero hybrid theory
  9. The curve Yn = Xℓ(Xm + 1) over finite fields II
  10. Uniqueness results for bodies of constant width in the hyperbolic plane
  11. A note on large Kakeya sets
  12. On static manifolds and related critical spaces with cyclic parallel Ricci tensor
  13. The motivic Igusa zeta function of a space monomial curve with a plane semigroup
  14. Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator
https://doi.org/10.1515/advgeom-2021-0017
Keywords for this article
Finite field; maximal curve; Kummer extension

Articles in the same Issue

  1. Frontmatter
  2. On vector bundles over reducible curves with a node
  3. Inscribed rectangle coincidences
  4. 𝔽p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
  5. Tetrahedral cages for unit discs
  6. When is M0,n(ℙ1,1) a Mori dream space?
  7. Rank-one isometries of CAT(0) cube complexes and their centralisers
  8. Wall-crossing in genus-zero hybrid theory
  9. The curve Yn = Xℓ(Xm + 1) over finite fields II
  10. Uniqueness results for bodies of constant width in the hyperbolic plane
  11. A note on large Kakeya sets
  12. On static manifolds and related critical spaces with cyclic parallel Ricci tensor
  13. The motivic Igusa zeta function of a space monomial curve with a plane semigroup
  14. Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator
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