论文标题
在kummer扩展上，无穷大的位置
On Kummer extensions with one place at infinity
论文作者
论文摘要
令$ k $为$ \ mathbb {f} _ {q} $的代数关闭。我们在曲线$ \ Mathcal $ \ Mathcal {x} $的唯一位置提供了weierstrass semigroup $ h（q_ \ infty）$的明确说明\ text {deg} f）= 1 $。结果，在某些情况下，我们确定$ h（q _ {\ infty}）$的frobenius编号和多重性，并且我们讨论了WeierStrass Semigroup $ h（q _ {\ infty}）$的足够条件，以使其对称。最后，我们表征了类型$（\ Mathcal {x}，q _ {\ infty}）$的某些最大城堡曲线。
Let $K$ be the algebraic closure of $\mathbb{F}_{q}$. We provide an explicit description of the Weierstrass semigroup $H(Q_\infty)$ at the only place at infinity $Q_{\infty}$ of the curve $\mathcal{X}$ defined by the Kummer extension with equation $y^m=f(x)$, where $f(x)\in K[x]$ is a polynomial satisfying $\gcd (m, \text{deg} f)=1$. As a consequence, we determine the Frobenius number and the multiplicity of $H(Q_{\infty})$ in some cases, and we discuss sufficient conditions for the Weierstrass semigroup $H(Q_{\infty})$ to be symmetric. Finally, we characterize certain maximal Castle curves of type $(\mathcal{X}, Q_{\infty})$.
