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Journals / Hagia Sophia Journal of Geometry / 2026 / Cilt: 4 Sayı: 1

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

Edoardo Ballico(University of Trento)0000-0002-1432-7413
Pages
17–19
Publication Date
2022-07-24
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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 Key Takeaways

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Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact: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 $D^-(q)$ .
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article

Ballico, 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/1490446

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References (8)

  1. Niederreiter, H., & Xing, C. (2001). Rational points on curves over finite fields: theory and applications, Cambridge University Press, Cambridge.
  2. Niederreiter, H., & Xing, C. (2009). Algebraic Geometry in Coding Theory and Cryptography, Princeton University Press, Princeton, NJ.
  3. 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.
  4. Stichtenoth, H. (2009). Algebraic function fields and codes, Second Edition. Springer-Verlag.
  5. Tsfasman, M., Vlădut, S., & Nogin, D. (2007). Algebraic Geometric Codes: Basic Notions, Mathematical Surveys and Monographs, 139.
  6. 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.
  7. 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).
  8. Beelen, P., & Montanucci, M. (2020). A bound for the number of points of space curves over finite fields. arXiv:2008.05748.