论文标题
具有较大序列的自动形态群的代数曲线
Algebraic curves with automorphism groups of large prime order
论文作者
论文摘要
令$ \ mathcal {x} $为在代数封闭的特征性特征$ p \ geq 0 $的代数$ g $属的代数曲线和$ q $ a prime divinding $ | \ mbox {aut}（aut}（aut}（\ mathcal {x}}））| $ $。我们说$ \ Mathcal {x} $是$ q $ -curve。 Homma证明了$ Q \ leq G+1 $或$ Q = 2G+1 $，然后分类$（2G+1）$ - 曲线。在本说明中，我们对$（g+1）$ - 曲线进行了分类，并完全表征$ q $ curves $ q = 2g+1，g+1 $的自动形态组。我们还以$ q = g，g-1 $的$ q $ curves给出了一些部分结果。
Let $\mathcal{X}$ be an algebraic curve of genus $g$ defined over an algebraically closed field $K$ of characteristic $p \geq 0$, and $q$ a prime dividing $|\mbox{Aut}(\mathcal{X})|$. We say that $\mathcal{X}$ is a $q$-curve. Homma proved that either $q \leq g+1$ or $q = 2g+1$, and classified $(2g+1)$-curves. In this note, we classify $(g+1)$-curves, and fully characterize the automorphism groups of $q$-curves for $q= 2g+1, g+1$. We also give some partial results on $q$-curves for $q = g, g-1$.
