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

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

Edoardo BALLİCO
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:Research Article
📍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

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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References (6)

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  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.