ScholarWorks@경상국립대학교

초록

We introduce the notion of a relative of the Hermitian curve of degree q+1$\sqrt{q}+1$ over Fq${\mathbb{F}}_q$, which is a plane curve defined by (xq,yq,zq)At(x,y,z)=0$\begin{array}{r}(x{<}^{>}\sqrt{q},y{<}^{>}\sqrt{q},z{<}^{>}\sqrt{q})A{<}^{>}t(x,y,z)=0\end{array}$with A is an element of GL(3,Fq)$A\in GL(3,{\mathbb{F}}_q)$, and we study their basic properties. One of the basic properties is that the number of Fq${\mathbb{F}}_q$-points of any relative of the Hermitian curve of degree q+1$\sqrt{q}+1$ is congruent to 1 modulo q$\sqrt{q}$. In the latter part of this paper, we classify those curves having two or more rational inflexions.

키워드