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

Authors : Edoardo BALLİCO

Pages : 17-19

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Publication Date : 2022-07-24

Article Type : Research Paper

Abstract :We consider the existence of smooth projective curves embedded over a fixed finite field $\mathbb{F}_q$ and such that their ratio $\#Xinsert ignore into journalissuearticles values(\mathbb {F}_q);/\deginsert ignore into journalissuearticles values(X);$ is large. We discuss the geometry of curves computing the Iihara constants $Ainsert ignore into journalissuearticles values(q);$ and $A^-insert ignore into journalissuearticles values(q);$ and relate it to upper and lower bound of the Homma constants $Dinsert ignore into journalissuearticles values(q);$ and $D^-insert ignore into journalissuearticles values(q);$ .
Keywords : Finite field, curve over a finite field, curves in projective spaces