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

Year 2022, Volume: 4 Issue: 1, 17 - 19, 24.07.2022

Edoardo Ballico

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 $D^-(q)$ .

Keywords

Finite field, curve over a finite field, curves in projective spaces

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