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Dergiler / Hagia Sophia Journal of Geometry / 2022 / Cilt: 4 - Sayı: 1

Embedded Projective Curves over a Finite Field and Homma Constant $D(q)$

Edoardo BALLİCO
Sayfa
17–19
Yayın Tarihi
2022-07-24
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We discuss the geometry of curves computing the Iihara constants $A(q)$ and $A^-(q)$ and relate it to upper and lower bound of the Homma constants $D(q)$ and $D^-(q)$ .

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We consider the existence of smooth projective curves embedded over a fixed finite field $\mathbb{F}_q$ and such that their ratio $\#X(\mathbb {F}_q)/\deg(X)$ is large.
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Temel Bulgular & Veri:We consider the existence of smooth projective curves embedded over a fixed finite field $\mathbb{F}_q$ and such that their ratio $\#X(\mathbb {F}_q)/\deg(X)$ is large.
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Sonuç & Katkı:We discuss the geometry of curves computing the Iihara constants $A(q)$ and $A^-(q)$ and relate it to upper and lower bound of the Homma constants $D(q)$ and $D^-(q)$ .
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Finite field · curve over a finite field · curves in projective spaces

Abstract

We consider the existence of smooth projective curves embedded over a fixed finite field $\mathbb{F}_q$ and such that their ratio $\#X(\mathbb {F}_q)/\deg(X)$ is large. We discuss the geometry of curves computing the Iihara constants $A(q)$ and $A^-(q)$ and relate it to upper and lower bound of the Homma constants $D(q)$ and $D^-(q)$ .

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Bu Makaleye Atıf Yap

BALLİCO, E. (2022). Embedded Projective Curves over a Finite Field and Homma Constant $D(q)$. Hagia Sophia Journal of Geometry, Cilt: 4 - Sayı: 1, 17–19. https://ajindex.com/articles/762892

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Kaynakça (6)

  1. Niederreiter, H., & Xing, C. (2001). Rational points on curves over finite fields: theory and applications, Cambridge University Press,
  2. Cambridge. Niederreiter, H., & Xing, C. (2009). Algebraic Geometry in Coding Theory and Cryptography, Princeton University Press,
  3. Princeton, NJ. Serre, J. P., Howe, E. W., Oesterlé, J., & Ritzenthaler, C. (2020). Rational points on curves over finite fields, Documents Mathématiques, 18, Société Mathématique de France, Paris. Stichtenoth, H. (2009).
  4. Algebraic function fields and codes, Second Edition.
  5. Springer-Verlag. Tsfasman, M., Vlădut, S., & Nogin, D. (2007). Algebraic Geometric Codes: Basic Notions, Mathematical Surveys and Monographs, 139. Homma, M. (2012). A bound on the number of points of a curve in a projective space over a finite field, Theory and Applications of Finite Fields, 597, 103-110.
  6. Beelen, P., Montanucci, M., & Vicino, L. (2022). On the constant D(q) defined by Homma. arXiv:2201.00602; accepted in Proceedings of the 18th Conference on Arithmetic, Geometry, Cryptography, and Coding Theory in the AMS book series Contemporary Mathematics (CONM). Beelen, P., & Montanucci, M. (2020). A bound for the number of points of space curves over finite fields. arXiv:2008.05748.