论文标题
普通的Fermat曲线的光滑商
Smooth quotients of generalized Fermat curves
论文作者
论文摘要
封闭的Riemann Surface $ S $称为$ $（p，n）$的广义费马特曲线，其中$ n，p \ geq 2 $是整数，如果$（p-1）（n-1）> 2 $，如果它承认了$ h \ cong {\ cong {\ mathb z} _ {零属，恰好$ n+1 $圆锥点，每个订单$ p $;在这种情况下，$ h $称为$ $ $（p，n）$的广义费马特集团。在这种情况下，众所周知，$ s $是非hyperelliptic的，$ h $是其独特的概括$ $ $ $（p，n）$的唯一通用费马特集团。同样，对于他们来说，显式方程是$ p $的经典费摩特曲线的光纤产品。对于$ p $ a Prime整数，我们描述了这些子组的$ k $ $ h $ $ h $在$ s $上自由作用，以及$ s/k $的代数方程式，并确定$ k $，以便$ s/k $是过度ellelliptic的。
A closed Riemann surface $S$ is called a generalized Fermat curve of type $(p,n)$, where $n,p \geq 2$ are integers such that $(p-1)(n-1)>2$, if it admits a group $H \cong {\mathbb Z}_{p}^{n}$ of conformal automorphisms with quotient orbifold $S/H$ of genus zero with exactly $n+1$ cone points, each one of order $p$; in this case $H$ is called a generalized Fermat group of type $(p,n)$. In this case, it is known that $S$ is non-hyperelliptic and that $H$ is its unique generalized Fermat group of type $(p,n)$. Also, explicit equations for them, as a fiber product of classical Fermat curves of degree $p$, are known. For $p$ a prime integer, we describe those subgroups $K$ of $H$ acting freely on $S$, together with algebraic equations for $S/K$, and determine those $K$ such that $S/K$ is hyperelliptic.
