论文标题
Hurwitz Moduli品种参数化代数曲线的GALOIS封面
Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve
论文作者
论文摘要
鉴于我们研究平滑，投射的曲线$ y $，有限的集团$ g $和一个正整数$ n $，我们研究流畅，适当的家庭$ x \ y \ times s \ to y \ times s \ to $ y $的$ y $的s $，以及galois group group insomorphic insomorphic to $ g $ n $ n $分支，分支为$ n $，由algebraic verailes $ n $ $ n $ n $ n $分支。当$ g $与微不足道的中心一起使用时，我们证明Hurwitz Space $ h^g_n（y）$是这个模量问题的典范变体，并明确构建了通用家庭。对于任意$ g $，我们证明$ h^g_n（y）$是一个粗糙的模量品种。对于$（y，y_0）$的尖头盖式封面的家庭，我们证明Hurwitz Space $ h^g_n（y，y_0）$是一种精美的模型品种，并明确构建了通用家庭，用于任意$ g $。我们使用代数拓扑的经典工具和复杂的代数几何形状。
Given a smooth, projective curve $Y$, a finite group $G$ and a positive integer $n$ we study smooth, proper families $X\to Y\times S\to S$ of Galois covers of $Y$ with Galois group isomorphic to $G$ branched in $n$ points, parameterized by algebraic varieties $S$. When $G$ is with trivial center we prove that the Hurwitz space $H^G_n(Y)$ is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary $G$ we prove that $H^G_n(Y)$ is a coarse moduli variety. For families of pointed Galois covers of $(Y,y_0)$ we prove that the Hurwitz space $H^G_n(Y,y_0)$ is a fine moduli variety, and construct explicitly the universal family, for arbitrary group $G$. We use classical tools of algebraic topology and of complex algebraic geometry.
